1 00:00:00,080 --> 00:00:01,670 The following content is provided 2 00:00:01,670 --> 00:00:03,820 under a Creative Commons license. 3 00:00:03,820 --> 00:00:06,550 Your support will help MIT OpenCourseWare continue 4 00:00:06,550 --> 00:00:10,160 to offer high quality educational resources for free. 5 00:00:10,160 --> 00:00:12,700 To make a donation or to view additional materials 6 00:00:12,700 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:17,327 at ocw.mit.edu. 8 00:00:24,950 --> 00:00:28,760 PROFESSOR: OK, in that case we can 9 00:00:28,760 --> 00:00:33,850 jump into the early universe. 10 00:00:33,850 --> 00:00:37,000 So on the opening slide here I have a picture 11 00:00:37,000 --> 00:00:40,210 of the Planck satellite, which is a satellite that 12 00:00:40,210 --> 00:00:44,810 was launched a few years ago dedicated to measuring 13 00:00:44,810 --> 00:00:47,199 the cosmic background radiation. 14 00:00:47,199 --> 00:00:48,740 Cosmic background radiation is really 15 00:00:48,740 --> 00:00:53,830 our biggest clue for the early history of the universe. 16 00:00:53,830 --> 00:00:56,780 The Planck satellite is actually the third satellite 17 00:00:56,780 --> 00:01:01,510 to go up completely dedicated to measuring the cosmic background 18 00:01:01,510 --> 00:01:02,500 radiation. 19 00:01:02,500 --> 00:01:06,380 The first was called COBE and then WMAP and now Planck. 20 00:01:06,380 --> 00:01:08,320 Planck is still in orbit. 21 00:01:08,320 --> 00:01:10,270 It actually is finished with its data-taking, 22 00:01:10,270 --> 00:01:12,400 although it's nowhere near finished 23 00:01:12,400 --> 00:01:14,480 with the analysis of that data. 24 00:01:14,480 --> 00:01:18,240 So they made one major data release last March, 25 00:01:18,240 --> 00:01:21,030 and there are still very important pieces of their data 26 00:01:21,030 --> 00:01:23,180 that I haven't looked at yet. 27 00:01:23,180 --> 00:01:25,490 And we'll be talking more about what exactly 28 00:01:25,490 --> 00:01:26,860 these satellites see. 29 00:01:29,800 --> 00:01:31,330 Onward. 30 00:01:31,330 --> 00:01:33,970 I want to begin by talking about the standard Big Bang, which 31 00:01:33,970 --> 00:01:36,640 will in fact be the main focus of this course. 32 00:01:36,640 --> 00:01:40,170 We'll probably spend about 2/3 of the course or so talking 33 00:01:40,170 --> 00:01:42,610 about the standard Big Bang and then move on 34 00:01:42,610 --> 00:01:45,590 to topics like inflation. 35 00:01:45,590 --> 00:01:50,120 That actually is, I think, a very sensible balance, 36 00:01:50,120 --> 00:01:56,690 because as you'll see once we get under studying inflation, 37 00:01:56,690 --> 00:01:59,096 it's a fairly straightforward thing once you know 38 00:01:59,096 --> 00:02:03,440 the basic equations coming out of standard cosmology. 39 00:02:03,440 --> 00:02:05,490 So I think spending about 2/3 of the term or so 40 00:02:05,490 --> 00:02:09,180 on the conventional cosmology before we get to inflation 41 00:02:09,180 --> 00:02:12,230 is very sensible, because that will set up all the principles 42 00:02:12,230 --> 00:02:14,480 that we'll be using later to discuss more 43 00:02:14,480 --> 00:02:17,260 advanced topics like inflation. 44 00:02:17,260 --> 00:02:20,640 The conventional Big Bang model is basically the theory 45 00:02:20,640 --> 00:02:23,430 that the universe as we know it began some 46 00:02:23,430 --> 00:02:26,000 13 to 14 billion years ago. 47 00:02:26,000 --> 00:02:29,200 And now we even have a pretty precise number 48 00:02:29,200 --> 00:02:32,780 to replace this 13 to 14 billion years. 49 00:02:32,780 --> 00:02:34,360 This is based on the Planck satellite 50 00:02:34,360 --> 00:02:36,920 combined with a few other pieces of information. 51 00:02:36,920 --> 00:02:42,740 The number is 13.82 billion years, plus or minus 0.05. 52 00:02:42,740 --> 00:02:44,860 So it's pretty well pinned down now, 53 00:02:44,860 --> 00:02:49,300 the age of the universe since the Big Bang. 54 00:02:49,300 --> 00:02:53,350 I should add, though, I put in the qualifier "the universe 55 00:02:53,350 --> 00:02:54,810 as we know it." 56 00:02:54,810 --> 00:02:58,500 What that really means is that I want to leave it out, 57 00:02:58,500 --> 00:03:00,850 because we don't really know that the universe began 58 00:03:00,850 --> 00:03:02,862 with what we call the Big Bang. 59 00:03:02,862 --> 00:03:04,820 So we have a very good picture of the Big Bang, 60 00:03:04,820 --> 00:03:07,490 and we're very confident that it happened 61 00:03:07,490 --> 00:03:10,850 and that we understand what it looked like. 62 00:03:10,850 --> 00:03:12,600 But whether or not anything came before it 63 00:03:12,600 --> 00:03:14,350 is a much more open question which I think 64 00:03:14,350 --> 00:03:15,660 is really completely open. 65 00:03:15,660 --> 00:03:19,640 I think we should not act like we know that the universe began 66 00:03:19,640 --> 00:03:21,444 with the Big Bang. 67 00:03:21,444 --> 00:03:23,610 And in fact later at the very end of the course when 68 00:03:23,610 --> 00:03:25,920 we discuss some of the implications of inflation 69 00:03:25,920 --> 00:03:28,000 and the multiverse, we'll see that there are 70 00:03:28,000 --> 00:03:31,510 strong suggestions that the Big Bang was perhaps not really 71 00:03:31,510 --> 00:03:33,710 the beginning of existence, but really 72 00:03:33,710 --> 00:03:38,330 just the beginning of our local universe, 73 00:03:38,330 --> 00:03:41,170 often called a pocket universe. 74 00:03:41,170 --> 00:03:42,370 OK. 75 00:03:42,370 --> 00:03:46,130 In any case, what the Big Bang theory tells 76 00:03:46,130 --> 00:03:49,370 us is that at least our region of the universe 77 00:03:49,370 --> 00:03:55,340 13.82 billion years ago was an extremely hot, dense, uniform 78 00:03:55,340 --> 00:04:00,490 soup of particles, which in the conventional standard Big Bang 79 00:04:00,490 --> 00:04:03,070 model filled literally all of space. 80 00:04:03,070 --> 00:04:05,430 And now we certainly believe it filled essentially all 81 00:04:05,430 --> 00:04:10,150 the space that we have access to uniformly. 82 00:04:10,150 --> 00:04:11,830 Now I should point out that this is 83 00:04:11,830 --> 00:04:16,890 contrary to a popular cartoon image of the Big Bang, which 84 00:04:16,890 --> 00:04:18,440 is just plain wrong. 85 00:04:18,440 --> 00:04:21,019 The cartoon image of the Big Bang 86 00:04:21,019 --> 00:04:24,385 is the image of a small egg of highly dense matter that 87 00:04:24,385 --> 00:04:27,760 then exploded and spewed out into empty space. 88 00:04:27,760 --> 00:04:30,910 That is not the scientific picture of the Big Bang. 89 00:04:30,910 --> 00:04:35,410 And the reason is not because it's illogical. 90 00:04:35,410 --> 00:04:39,010 It's hard to know what's logical or illogical in this context. 91 00:04:39,010 --> 00:04:42,760 But simply based on what we see, if there 92 00:04:42,760 --> 00:04:46,370 was a small egg that exploded into empty space, 93 00:04:46,370 --> 00:04:48,157 you would certainly expect that today you 94 00:04:48,157 --> 00:04:50,740 would see something different if you were looking toward where 95 00:04:50,740 --> 00:04:54,190 the egg was versus looking the opposite direction. 96 00:04:54,190 --> 00:04:56,290 But we don't see any effect like that. 97 00:04:56,290 --> 00:04:59,160 When we look around the sky, the universal 98 00:04:59,160 --> 00:05:03,197 looks completely uniform, on average, in all directions 99 00:05:03,197 --> 00:05:04,530 to very high degree of accuracy. 100 00:05:04,530 --> 00:05:08,160 I'll talk a little bit more precisely later. 101 00:05:08,160 --> 00:05:11,620 So we don't see any sign of an egg having happened anywhere. 102 00:05:11,620 --> 00:05:13,100 Rather the Big Bang seems to have 103 00:05:13,100 --> 00:05:14,350 happened everywhere uniformly. 104 00:05:17,290 --> 00:05:19,070 OK. 105 00:05:19,070 --> 00:05:21,380 The Big Bang describes a number of important things, 106 00:05:21,380 --> 00:05:23,940 and we'll be talking about this more as the course goes on. 107 00:05:26,470 --> 00:05:29,580 It describes how the early universe expanded and cooled-- 108 00:05:29,580 --> 00:05:32,700 and will be spending a fair amount of time understanding 109 00:05:32,700 --> 00:05:35,330 the details behind those words. 110 00:05:35,330 --> 00:05:37,510 The point is that the Big Bang really 111 00:05:37,510 --> 00:05:42,100 is a very precise model based on very simple assumptions. 112 00:05:42,100 --> 00:05:44,020 You basically assume that the early universe 113 00:05:44,020 --> 00:05:47,550 was filled by a hot gas in thermal equilibrium. 114 00:05:47,550 --> 00:05:50,250 And that this gas was expanding and being pulled back 115 00:05:50,250 --> 00:05:52,120 by gravity. 116 00:05:52,120 --> 00:05:55,060 And from those simple ideas you can really calculate-- 117 00:05:55,060 --> 00:05:57,450 and we'll learn how to calculate-- 118 00:05:57,450 --> 00:06:00,190 how fast the universe would have been expanding at any given 119 00:06:00,190 --> 00:06:02,550 instant of time, what the temperature would have been 120 00:06:02,550 --> 00:06:05,590 at any given instant of time, what the density of matter 121 00:06:05,590 --> 00:06:08,810 would have been at any instant of time. 122 00:06:08,810 --> 00:06:10,800 So all the details really can be calculated 123 00:06:10,800 --> 00:06:13,290 from some rather simple ideas, and we'll 124 00:06:13,290 --> 00:06:15,760 have fun exploring that. 125 00:06:15,760 --> 00:06:18,260 The Big Bang also talks about how the light chemical 126 00:06:18,260 --> 00:06:19,610 elements formed. 127 00:06:19,610 --> 00:06:21,090 And that actually is the main topic 128 00:06:21,090 --> 00:06:24,934 of Steve Weinberg's book "The First Three Minutes." 129 00:06:24,934 --> 00:06:27,350 Because that was more or less the time period during which 130 00:06:27,350 --> 00:06:31,080 the chemical elements formed. 131 00:06:31,080 --> 00:06:34,990 It turns out that most of the elements in the universe 132 00:06:34,990 --> 00:06:39,530 did not form in the Big Bang, but formed much later 133 00:06:39,530 --> 00:06:41,340 in the interior of stars. 134 00:06:41,340 --> 00:06:44,010 And those elements are then strewn out into space 135 00:06:44,010 --> 00:06:47,660 in supernova explosions and collected into later generation 136 00:06:47,660 --> 00:06:51,130 stars, of which our sun would be one. 137 00:06:51,130 --> 00:06:54,780 So the stuff that we're made out of was actually not produced 138 00:06:54,780 --> 00:06:56,850 in the Big Bang, but rather was produced 139 00:06:56,850 --> 00:07:01,850 in the interior of some distant star that exploded long ago. 140 00:07:01,850 --> 00:07:04,960 And maybe many stars, whose material 141 00:07:04,960 --> 00:07:08,190 collected to form our solar system. 142 00:07:08,190 --> 00:07:11,340 Nonetheless, most of the matter in the universe-- as opposed 143 00:07:11,340 --> 00:07:13,609 to most of the different kinds of elements-- 144 00:07:13,609 --> 00:07:14,650 did form in the Big Bang. 145 00:07:14,650 --> 00:07:15,780 Most of the matter in the universe 146 00:07:15,780 --> 00:07:16,970 is just hydrogen and helium. 147 00:07:19,830 --> 00:07:23,180 About five different isotopes of hydrogen, helium, and lithium 148 00:07:23,180 --> 00:07:26,400 were primarily formed in the Big Bang, 149 00:07:26,400 --> 00:07:30,470 and because we do have this detailed picture of the Big 150 00:07:30,470 --> 00:07:32,340 Bang that we'll be learning about, 151 00:07:32,340 --> 00:07:34,420 it's possible to actually calculate 152 00:07:34,420 --> 00:07:38,200 the predicted abundances of those different isotopes. 153 00:07:38,200 --> 00:07:41,400 And the predictions agree very well with the observations. 154 00:07:41,400 --> 00:07:44,320 And this is certainly one of the major confirmations 155 00:07:44,320 --> 00:07:48,660 we have that this picture of the Big Bang is correct. 156 00:07:48,660 --> 00:07:51,620 We can predict what the abundance of helium-3 157 00:07:51,620 --> 00:07:53,890 should be, and we measure it, and it agrees. 158 00:07:53,890 --> 00:07:55,155 It's rather marvelous. 159 00:07:58,600 --> 00:08:00,412 Finally-- and this subject we're not 160 00:08:00,412 --> 00:08:01,870 going to talk about much because it 161 00:08:01,870 --> 00:08:04,250 goes beyond the level of complexity 162 00:08:04,250 --> 00:08:05,690 that the course is going to have-- 163 00:08:05,690 --> 00:08:07,690 but finally the Big Bang does discuss 164 00:08:07,690 --> 00:08:10,540 how the matter ultimately congealed to form stars, 165 00:08:10,540 --> 00:08:12,460 galaxies, clusters of galaxies. 166 00:08:12,460 --> 00:08:14,460 We'll talk about that a little bit, 167 00:08:14,460 --> 00:08:17,370 but we won't really follow that very far. 168 00:08:17,370 --> 00:08:20,440 That is still in principle a work in progress. 169 00:08:20,440 --> 00:08:23,330 People do not understand everything about galaxies. 170 00:08:23,330 --> 00:08:25,330 But the general picture of that-- it started out 171 00:08:25,330 --> 00:08:27,190 with an almost uniform universe, and then 172 00:08:27,190 --> 00:08:31,020 the lumps congealed to form the galaxies and the structures-- 173 00:08:31,020 --> 00:08:35,059 we say certainly seems to be a working picture. 174 00:08:35,059 --> 00:08:38,799 And one can understand a lot about the universe 175 00:08:38,799 --> 00:08:42,020 from this very simple picture. 176 00:08:42,020 --> 00:08:43,429 OK what I want to talk about next 177 00:08:43,429 --> 00:08:45,950 is what the conventional Big Bang theory does not 178 00:08:45,950 --> 00:08:49,430 talk about, where new ideas like inflation come in. 179 00:08:52,440 --> 00:08:54,800 First of all, the conventional Big Bang theory 180 00:08:54,800 --> 00:08:58,460 does not say anything about what caused the expansion. 181 00:08:58,460 --> 00:09:02,280 It really is only a theory of the aftermath of a bang. 182 00:09:05,830 --> 00:09:09,700 In the scientific version of the Big Bang, 183 00:09:09,700 --> 00:09:12,350 the universe starts with everything already expanding 184 00:09:12,350 --> 00:09:14,800 with no explanation of how that expansion started. 185 00:09:14,800 --> 00:09:18,550 That's not part of the Big Bang theory. 186 00:09:18,550 --> 00:09:21,440 So the scientific version of the Big Bang theory 187 00:09:21,440 --> 00:09:23,100 is not really a theory of a bang. 188 00:09:23,100 --> 00:09:26,790 It's really the theory of the aftermath of a bang. 189 00:09:26,790 --> 00:09:29,430 In addition, and maybe in a similar vein, 190 00:09:29,430 --> 00:09:31,020 the conventional Big Bang theory says 191 00:09:31,020 --> 00:09:33,850 nothing about where all the matter came from. 192 00:09:33,850 --> 00:09:36,690 The theory really assumes that for every particle that we 193 00:09:36,690 --> 00:09:39,210 see in the universe today, there was 194 00:09:39,210 --> 00:09:41,950 at the very beginning at least some precursor particle, 195 00:09:41,950 --> 00:09:46,530 if not the same particle, with no explanation of where 196 00:09:46,530 --> 00:09:49,730 all those particles came from. 197 00:09:49,730 --> 00:09:53,130 In short, what I like to say is that the Big Bang says nothing 198 00:09:53,130 --> 00:09:55,580 about what banged, why it banged, 199 00:09:55,580 --> 00:09:58,100 or what happened before it banged. 200 00:09:58,100 --> 00:10:00,530 It really has no bang in the Big Bang. 201 00:10:00,530 --> 00:10:04,060 It's a bangless theory, despite its name. 202 00:10:04,060 --> 00:10:07,320 Inflation, it turns out, fills in possible answers, 203 00:10:07,320 --> 00:10:11,850 very plausible answers, for many of these questions. 204 00:10:11,850 --> 00:10:13,750 And that's what I'll be talking about mainly 205 00:10:13,750 --> 00:10:14,767 for the rest of today. 206 00:10:14,767 --> 00:10:16,350 And as I said, in terms of the course, 207 00:10:16,350 --> 00:10:18,815 it's where we'll be aiming to get about 2/3 of the way 208 00:10:18,815 --> 00:10:19,690 through the semester. 209 00:10:22,380 --> 00:10:24,890 What is cosmic inflation? 210 00:10:24,890 --> 00:10:28,160 It's basically a minor modification, 211 00:10:28,160 --> 00:10:30,070 in terms of the overall scheme of things, 212 00:10:30,070 --> 00:10:32,980 of the standard Big Bang theory. 213 00:10:32,980 --> 00:10:35,900 And the best word to describe it is a word that I think 214 00:10:35,900 --> 00:10:38,220 was invented by Hollywood-- inflation 215 00:10:38,220 --> 00:10:43,340 is a prequel to the conventional Big Bang theory. 216 00:10:43,340 --> 00:10:47,060 It's a short description of what happened before, 217 00:10:47,060 --> 00:10:49,770 immediately before, the Big Bang. 218 00:10:49,770 --> 00:10:51,420 So inflation really is an explanation 219 00:10:51,420 --> 00:10:53,660 of the bang of the Big Bang in the sense 220 00:10:53,660 --> 00:10:57,670 that it does provide a theory of the propulsion that 221 00:10:57,670 --> 00:11:03,490 drove the universe into this humongous episode of expansion 222 00:11:03,490 --> 00:11:05,440 which we call the Big Bang. 223 00:11:05,440 --> 00:11:07,730 And it does it in terms of something 224 00:11:07,730 --> 00:11:11,350 that I like to think of as a miracle of physics. 225 00:11:11,350 --> 00:11:17,230 When I use the word "miracle" in this context-- referring 226 00:11:17,230 --> 00:11:20,030 to a miracle in the scientific sense-- 227 00:11:20,030 --> 00:11:23,760 simply something that's so surprising that I think 228 00:11:23,760 --> 00:11:26,340 it merits being called a miracle even though it's something 229 00:11:26,340 --> 00:11:28,834 that's a part of the laws of physics. 230 00:11:28,834 --> 00:11:31,000 There are just a few features of the laws of physics 231 00:11:31,000 --> 00:11:32,770 that are actually crucial to inflation-- 232 00:11:32,770 --> 00:11:35,180 I'll be talking about two of them-- 233 00:11:35,180 --> 00:11:37,770 which I consider miracles simply because-- well, 234 00:11:37,770 --> 00:11:39,830 mainly because when I was an undergrad nobody 235 00:11:39,830 --> 00:11:41,670 talked about them at all. 236 00:11:41,670 --> 00:11:43,970 They were just not part of physics then, 237 00:11:43,970 --> 00:11:45,460 even though they really were. 238 00:11:45,460 --> 00:11:47,610 They just weren't parts of physics people 239 00:11:47,610 --> 00:11:49,480 noticed and talked about. 240 00:11:49,480 --> 00:11:51,550 So the miracle of physics I'm talking about here 241 00:11:51,550 --> 00:11:53,190 is something which actually is known 242 00:11:53,190 --> 00:11:56,790 since the time of Einstein's general relativity-- 243 00:11:56,790 --> 00:11:59,540 that gravity is not always attractive. 244 00:11:59,540 --> 00:12:02,140 Gravity can act repulsively. 245 00:12:02,140 --> 00:12:08,650 And Einstein introduced this in 1916, I guess, 246 00:12:08,650 --> 00:12:12,160 in the form of what he called his cosmological constant. 247 00:12:12,160 --> 00:12:16,280 And the original motivation of modifying 248 00:12:16,280 --> 00:12:19,300 the equations of general relativity to allow this 249 00:12:19,300 --> 00:12:23,480 was because Einstein thought that the universe was static. 250 00:12:23,480 --> 00:12:25,420 And he realized that ordinary gravity 251 00:12:25,420 --> 00:12:27,711 would cause the universe to collapse if it were static. 252 00:12:27,711 --> 00:12:29,330 It couldn't remain static. 253 00:12:29,330 --> 00:12:32,740 So he introduced this cosmological constant term 254 00:12:32,740 --> 00:12:36,830 to balance the overall attraction of ordinary gravity 255 00:12:36,830 --> 00:12:40,560 to be able to build a static model of the universe. 256 00:12:40,560 --> 00:12:42,920 As you'll soon be learning, that's dead wrong. 257 00:12:42,920 --> 00:12:45,761 That's not what the universe looks like at all. 258 00:12:45,761 --> 00:12:47,260 But the fact that general relativity 259 00:12:47,260 --> 00:12:50,214 can support this gravitation repulsion, still 260 00:12:50,214 --> 00:12:51,880 being consistent with all the principles 261 00:12:51,880 --> 00:12:54,440 that general relativity incorporates, 262 00:12:54,440 --> 00:12:56,600 is the important thing which Einstein 263 00:12:56,600 --> 00:13:00,890 himself did discover in this context. 264 00:13:00,890 --> 00:13:05,530 And inflation takes advantage of this possibility, 265 00:13:05,530 --> 00:13:08,330 within the context of general relativity, 266 00:13:08,330 --> 00:13:11,510 to let gravity be the repulsive force that 267 00:13:11,510 --> 00:13:14,320 drove the universe into the period of expansion 268 00:13:14,320 --> 00:13:17,830 that we call the Big Bang. 269 00:13:17,830 --> 00:13:20,090 And in fact when one combines general relativity 270 00:13:20,090 --> 00:13:25,290 with conventional ideas now in particle physics, 271 00:13:25,290 --> 00:13:27,530 there really is a pretty clear indication, 272 00:13:27,530 --> 00:13:30,410 I should say-- not quite a prediction-- but a pretty clear 273 00:13:30,410 --> 00:13:33,830 indication that at very high energy densities, 274 00:13:33,830 --> 00:13:37,660 one expects to find states of matter which literally turn 275 00:13:37,660 --> 00:13:41,794 gravity on its head and cause gravity to become repulsive. 276 00:13:41,794 --> 00:13:44,210 In terms of the details which we'll be learning about more 277 00:13:44,210 --> 00:13:48,470 later, what it takes to produce gravitational repulsion 278 00:13:48,470 --> 00:13:51,090 is a negative pressure. 279 00:13:51,090 --> 00:13:53,770 According to general relativity, it turns out-- 280 00:13:53,770 --> 00:13:57,350 and we'll be talking more about this later-- both pressures 281 00:13:57,350 --> 00:14:00,660 and energy densities can produce gravitational fields. 282 00:14:00,660 --> 00:14:03,710 Unlike Newtonian physics, where it's only mass densities 283 00:14:03,710 --> 00:14:06,800 that produce gravitational fields. 284 00:14:06,800 --> 00:14:08,610 And the positive pressure produces 285 00:14:08,610 --> 00:14:10,680 an attractive gravitational field, 286 00:14:10,680 --> 00:14:13,320 which is what you would probably guess if somebody just 287 00:14:13,320 --> 00:14:14,300 asked you to guess. 288 00:14:14,300 --> 00:14:16,300 Positive pressures are sort of normal pressures, 289 00:14:16,300 --> 00:14:19,110 and attractive gravity is normal gravity. 290 00:14:19,110 --> 00:14:22,110 So normal pressures produce normal gravity. 291 00:14:22,110 --> 00:14:25,360 But it is possible to have negative pressures, 292 00:14:25,360 --> 00:14:28,040 and negative pressures produce repulsive gravity. 293 00:14:28,040 --> 00:14:31,845 That's the secret of what makes inflation possible. 294 00:14:34,780 --> 00:14:38,720 So inflation proposes that at least a small patch 295 00:14:38,720 --> 00:14:41,850 of this repulsive gravity material 296 00:14:41,850 --> 00:14:44,820 existed in the early universe. 297 00:14:44,820 --> 00:14:47,110 We don't really know exactly when 298 00:14:47,110 --> 00:14:49,344 in the history of the universe inflation happened, 299 00:14:49,344 --> 00:14:51,510 which is another way of saying we don't know exactly 300 00:14:51,510 --> 00:14:54,840 at what energy scale inflation happened. 301 00:14:54,840 --> 00:14:57,657 But a very logical, plausible choice-- 302 00:14:57,657 --> 00:14:59,990 I don't know if logical is the right word, but plausible 303 00:14:59,990 --> 00:15:02,090 is a good word-- very plausible choice 304 00:15:02,090 --> 00:15:04,840 for when inflation might have happened, 305 00:15:04,840 --> 00:15:07,580 would be when the energy scales of the universe where 306 00:15:07,580 --> 00:15:10,520 at the scale of grand unified theories. 307 00:15:10,520 --> 00:15:13,340 Grand unified theories-- we'll talk about a little bit later-- 308 00:15:13,340 --> 00:15:15,700 are theories which unify the weak, strong, 309 00:15:15,700 --> 00:15:17,990 and electromagnetic interactions into 310 00:15:17,990 --> 00:15:19,950 a single unified interaction. 311 00:15:19,950 --> 00:15:23,600 And that unification occurs at a typical energy of about 10 312 00:15:23,600 --> 00:15:27,830 to the 16 GeV, where GeV, in case you don't know, 313 00:15:27,830 --> 00:15:30,150 is about the mass-- or the energy 314 00:15:30,150 --> 00:15:32,130 equivalent of the mass-- of a proton. 315 00:15:32,130 --> 00:15:33,630 So we're talking about energies that 316 00:15:33,630 --> 00:15:37,960 are about 10 to the 16 times the equivalent energy of a proton 317 00:15:37,960 --> 00:15:39,880 mass. 318 00:15:39,880 --> 00:15:46,330 And at those energies we think that these states that 319 00:15:46,330 --> 00:15:49,340 create repulsive gravity are very likely to exist. 320 00:15:49,340 --> 00:15:51,400 And if that happened at that scale, 321 00:15:51,400 --> 00:15:52,790 the initial patch would only have 322 00:15:52,790 --> 00:15:55,450 to be the ridiculously small size of about 10 323 00:15:55,450 --> 00:15:58,460 to the minus 28 centimeters across 324 00:15:58,460 --> 00:16:01,180 to be able to lead ultimately to the creation of everything 325 00:16:01,180 --> 00:16:04,405 that we see on the vast scale at which we see it. 326 00:16:08,190 --> 00:16:12,170 The patch certainly does not have to be the entire universe. 327 00:16:12,170 --> 00:16:13,890 And it could in fact be incredibly rare, 328 00:16:13,890 --> 00:16:17,250 because one thinks that outside of that patch essentially 329 00:16:17,250 --> 00:16:18,850 nothing will happen interesting. 330 00:16:18,850 --> 00:16:22,400 So we expect that the universe that we observe today 331 00:16:22,400 --> 00:16:25,280 would be entirely the consequence of such a patch. 332 00:16:27,960 --> 00:16:30,110 The gravitational repulsion created 333 00:16:30,110 --> 00:16:33,360 by this small patch of repulsive gravity material 334 00:16:33,360 --> 00:16:36,780 would be then the driving force of the Big Bang, 335 00:16:36,780 --> 00:16:41,500 and it would cause the region to undergo exponential expansion. 336 00:16:41,500 --> 00:16:43,820 And by exponential expansion, as you probably know, 337 00:16:43,820 --> 00:16:45,776 it means that there's a certain doubling time, 338 00:16:45,776 --> 00:16:48,150 and if you wait the same amount of time it doubles again. 339 00:16:48,150 --> 00:16:50,500 If you wait the same amount of time, it doubles again. 340 00:16:50,500 --> 00:16:54,230 And because these doublings build up so dramatically, 341 00:16:54,230 --> 00:16:57,945 it doesn't take very much time to build the whole universe. 342 00:16:57,945 --> 00:17:02,340 In about 100 doublings, this tiny patch 343 00:17:02,340 --> 00:17:04,569 of 10 to the minus 28 centimeters 344 00:17:04,569 --> 00:17:07,000 can become large enough not to be the universe, 345 00:17:07,000 --> 00:17:12,109 but to be a small marble size region, which will then 346 00:17:12,109 --> 00:17:14,440 ultimately become the observed universe 347 00:17:14,440 --> 00:17:20,504 as it continues to coast outward after inflation ends. 348 00:17:20,504 --> 00:17:22,420 So the doubling time would be incredibly small 349 00:17:22,420 --> 00:17:25,670 if this was all happening at the grand unified theory 350 00:17:25,670 --> 00:17:28,940 set of numbers-- 10 to the minus 37 seconds, which 351 00:17:28,940 --> 00:17:32,840 is pretty fast. 352 00:17:32,840 --> 00:17:34,450 The patch would expand exponentially 353 00:17:34,450 --> 00:17:38,300 by at least a factor of about 10 to the 28, which as I mentioned 354 00:17:38,300 --> 00:17:42,672 takes only about 100 doublings, and could 355 00:17:42,672 --> 00:17:43,630 expand to be much more. 356 00:17:43,630 --> 00:17:44,930 There's no cut off there. 357 00:17:44,930 --> 00:17:46,610 If there's more expansion than we 358 00:17:46,610 --> 00:17:48,690 need to produce our universe, it just 359 00:17:48,690 --> 00:17:50,960 means that the patch of universe that we're living in 360 00:17:50,960 --> 00:17:52,800 is larger than we see. 361 00:17:52,800 --> 00:17:54,320 But that's OK. 362 00:17:54,320 --> 00:17:56,880 Everything that we see looks uniform as far as we can see, 363 00:17:56,880 --> 00:17:58,879 and how much there is beyond that we really just 364 00:17:58,879 --> 00:18:00,150 have no way of knowing. 365 00:18:00,150 --> 00:18:02,370 So larger amounts of inflation are 366 00:18:02,370 --> 00:18:05,399 perfectly consistent with what we see. 367 00:18:05,399 --> 00:18:07,690 The amount of time it would take would only be about 10 368 00:18:07,690 --> 00:18:11,160 to the minus 35 seconds, which is just 100 times 10 369 00:18:11,160 --> 00:18:14,920 to the minus 37 if you can do that complicated arithmetic 370 00:18:14,920 --> 00:18:16,800 in your head. 371 00:18:16,800 --> 00:18:20,320 And the region that's destined to become our presently 372 00:18:20,320 --> 00:18:22,430 observed universe at the end of inflation 373 00:18:22,430 --> 00:18:25,425 would have been only about the size of a marble-- about one 374 00:18:25,425 --> 00:18:26,550 centimeter or so across. 375 00:18:30,830 --> 00:18:32,550 Now what ends inflation is the fact 376 00:18:32,550 --> 00:18:36,190 that this repulsive gravity material is unstable. 377 00:18:36,190 --> 00:18:40,150 So it decays, using the word decay in the same sense 378 00:18:40,150 --> 00:18:43,022 that a radioactive substance decays. 379 00:18:43,022 --> 00:18:44,480 It doesn't necessarily mean exactly 380 00:18:44,480 --> 00:18:47,030 that it rots like an apple decays, 381 00:18:47,030 --> 00:18:49,760 but it means that it turns into other kinds of material. 382 00:18:49,760 --> 00:18:51,870 And in particular, it turned into material 383 00:18:51,870 --> 00:18:55,500 which is no longer gravitationally repulsive. 384 00:18:55,500 --> 00:18:59,880 So the gravitational repulsion ends, and in fact the particles 385 00:18:59,880 --> 00:19:02,520 produced by this energy that's released 386 00:19:02,520 --> 00:19:05,570 at the end of inflation become the hot soup 387 00:19:05,570 --> 00:19:07,490 of the conventional Big Bang. 388 00:19:07,490 --> 00:19:10,830 And this is where the prequel ends, 389 00:19:10,830 --> 00:19:14,030 and the main feature begins-- the conventional Big Bang 390 00:19:14,030 --> 00:19:15,060 theory. 391 00:19:15,060 --> 00:19:20,470 The role of inflation is just to set up the initial conditions 392 00:19:20,470 --> 00:19:22,500 for the conventional Big Bang theory. 393 00:19:25,850 --> 00:19:28,270 Now there's a little caveat here. 394 00:19:28,270 --> 00:19:32,290 Inflation ends because the material is unstable, 395 00:19:32,290 --> 00:19:34,350 but it only ends almost everywhere, not 396 00:19:34,350 --> 00:19:35,760 quite everywhere. 397 00:19:35,760 --> 00:19:37,800 And this is basically the way exponentials work. 398 00:19:37,800 --> 00:19:41,280 And we'll come back to this when we talk about the late time 399 00:19:41,280 --> 00:19:45,950 behavior and the idea of eternal inflation. 400 00:19:45,950 --> 00:19:48,800 This repulsive gravity material decays, 401 00:19:48,800 --> 00:19:51,710 but it decays like a radioactive substance-- which is also 402 00:19:51,710 --> 00:19:54,570 an exponential-- as a half life. 403 00:19:54,570 --> 00:19:56,670 But no matter how many half lives you wait, 404 00:19:56,670 --> 00:20:00,160 there's still a tiny little bit, a tiny fraction that remains. 405 00:20:00,160 --> 00:20:03,000 And that turns out to be important for the idea 406 00:20:03,000 --> 00:20:05,820 that in many cases inflation never completely ends. 407 00:20:05,820 --> 00:20:09,190 We'll come back to that. 408 00:20:09,190 --> 00:20:12,100 So I want to talk more about what goes on 409 00:20:12,100 --> 00:20:15,280 during this exponential expansion phase. 410 00:20:15,280 --> 00:20:18,360 There's a very peculiar feature of this inflation-- 411 00:20:18,360 --> 00:20:20,560 this exponential expansion driven 412 00:20:20,560 --> 00:20:24,800 by repulsive gravity-- which is that while it's happening, 413 00:20:24,800 --> 00:20:28,020 the mass density or energy density 414 00:20:28,020 --> 00:20:32,030 of the inflating material-- this repulsive gravity material-- 415 00:20:32,030 --> 00:20:33,820 does not decrease. 416 00:20:33,820 --> 00:20:36,075 You would think that if something doubled in radius, 417 00:20:36,075 --> 00:20:38,770 it would multiply by a factor of eight in volume. 418 00:20:38,770 --> 00:20:40,770 You would think the energy density would go down 419 00:20:40,770 --> 00:20:42,330 by a factor of eight. 420 00:20:42,330 --> 00:20:44,950 And that certainly happens for ordinary particles. 421 00:20:44,950 --> 00:20:46,575 It's certainly what would happen if you 422 00:20:46,575 --> 00:20:48,320 had a gas, an ordinary gas, that you just 423 00:20:48,320 --> 00:20:50,460 allowed to expand by a factor of two 424 00:20:50,460 --> 00:20:54,222 in radius-- the density would go down by a factor of eight 425 00:20:54,222 --> 00:20:56,860 with volumes of cubes of distances. 426 00:20:56,860 --> 00:20:59,890 But this peculiar repulsive gravity material actually 427 00:20:59,890 --> 00:21:03,450 expands at a constant density. 428 00:21:03,450 --> 00:21:06,910 Now that sounds like it must violate conservation of energy, 429 00:21:06,910 --> 00:21:09,860 because it really does mean that the total amount of energy 430 00:21:09,860 --> 00:21:12,550 inside this expanding volume is increasing. 431 00:21:12,550 --> 00:21:15,310 The energy per volume is remaining constant, 432 00:21:15,310 --> 00:21:20,790 and the volume is getting bigger and bigger exponentially. 433 00:21:20,790 --> 00:21:26,260 So the claim is that I've not gone crazy, that this actually 434 00:21:26,260 --> 00:21:29,120 is consistent with the laws of physics as we know them. 435 00:21:29,120 --> 00:21:32,010 And that it is consistent with conservation of energy. 436 00:21:32,010 --> 00:21:35,090 Conservation of energy really is a sacred principle of physics. 437 00:21:35,090 --> 00:21:38,650 We don't know of anything in nature that violates this 438 00:21:38,650 --> 00:21:40,245 principle of conservation of energy, 439 00:21:40,245 --> 00:21:44,000 that energy ultimately cannot be either made or destroyed, 440 00:21:44,000 --> 00:21:47,102 that the total amount of energy is basically fixed. 441 00:21:47,102 --> 00:21:49,060 So it sounds like there's a contradiction here. 442 00:21:49,060 --> 00:21:50,059 How do we get out of it? 443 00:21:50,059 --> 00:21:51,970 What's the resolution? 444 00:21:51,970 --> 00:21:56,340 Well, this requires my second miracle of physics. 445 00:21:56,340 --> 00:21:58,157 Energy-- it really is exactly conserved. 446 00:21:58,157 --> 00:22:00,240 I'm not going to tell you about any miracles which 447 00:22:00,240 --> 00:22:02,070 changed that. 448 00:22:02,070 --> 00:22:07,320 But the catch here is that energies are not 449 00:22:07,320 --> 00:22:09,060 necessarily positive. 450 00:22:09,060 --> 00:22:11,560 There are things that have negative energies. 451 00:22:11,560 --> 00:22:14,370 And in particular, the gravitational field 452 00:22:14,370 --> 00:22:16,870 has a negative energy. 453 00:22:16,870 --> 00:22:21,460 This statement by the way is true both in Newtonian physics 454 00:22:21,460 --> 00:22:24,630 and in general relativity. 455 00:22:24,630 --> 00:22:25,930 We'll prove it later. 456 00:22:28,940 --> 00:22:34,630 I might just say quickly if some of you 457 00:22:34,630 --> 00:22:38,400 have learned in an E&M course how to talk about and calculate 458 00:22:38,400 --> 00:22:42,810 the energy density of an electrostatic field-- probably 459 00:22:42,810 --> 00:22:44,800 many of you have, maybe all of you 460 00:22:44,800 --> 00:22:48,810 have-- the energy density of an electrostatic field 461 00:22:48,810 --> 00:22:52,510 is a constant times the square of the electric field strength. 462 00:22:52,510 --> 00:22:56,420 And you can prove that energy is exactly the energy 463 00:22:56,420 --> 00:22:57,880 that you need to put into a system 464 00:22:57,880 --> 00:23:00,088 to create an electric field of a given configuration. 465 00:23:02,820 --> 00:23:05,390 If you think about Newton's law of gravity 466 00:23:05,390 --> 00:23:07,192 and compare it with Coulomb's law, 467 00:23:07,192 --> 00:23:08,983 you realize that it really is the same law, 468 00:23:08,983 --> 00:23:11,320 except they have a different constant in front of them. 469 00:23:11,320 --> 00:23:14,370 They're both inverse square laws in proportion 470 00:23:14,370 --> 00:23:16,850 to the two charges, where in the case of gravity 471 00:23:16,850 --> 00:23:20,310 it's the masses that play the role of charges. 472 00:23:20,310 --> 00:23:22,075 But they have opposite signs. 473 00:23:22,075 --> 00:23:25,390 Two positive charges, as we all know we tell each other, 474 00:23:25,390 --> 00:23:28,070 two positive masses attract each other. 475 00:23:28,070 --> 00:23:29,980 So in fact the very same argument 476 00:23:29,980 --> 00:23:32,590 which allows you to calculate the energy density of a Coulomb 477 00:23:32,590 --> 00:23:36,810 field can allow you to calculate the energy 478 00:23:36,810 --> 00:23:40,150 density of a Newtonian gravitational field-- still 479 00:23:40,150 --> 00:23:43,910 sticking to Newtonian physics-- and this change 480 00:23:43,910 --> 00:23:45,660 in sign of the force just carries through. 481 00:23:45,660 --> 00:23:48,810 It changes the signs of all the work that's being done, 482 00:23:48,810 --> 00:23:51,110 and you get the negative answer that 483 00:23:51,110 --> 00:23:53,732 is the correct answer for Newtonian gravity. 484 00:23:53,732 --> 00:23:55,940 The energy density of a Newtonian gravitational field 485 00:23:55,940 --> 00:23:56,810 is negative. 486 00:23:56,810 --> 00:23:59,490 And the same is true in general relativity 487 00:23:59,490 --> 00:24:02,210 in a more subtle way. 488 00:24:02,210 --> 00:24:06,510 So what that means in terms of conservation of energy 489 00:24:06,510 --> 00:24:09,990 is that we can have more and more matter, more 490 00:24:09,990 --> 00:24:12,870 and more energy building up in the form of ordinary matter-- 491 00:24:12,870 --> 00:24:15,610 which is what happens during inflation-- as long as there's 492 00:24:15,610 --> 00:24:18,750 a compensating amount of negative energy 493 00:24:18,750 --> 00:24:21,420 that's created in the gravitational field which 494 00:24:21,420 --> 00:24:24,530 is filling this ever larger region of space. 495 00:24:24,530 --> 00:24:28,380 And that's exactly what happens in inflation. 496 00:24:28,380 --> 00:24:31,640 The positive energy of this repulsive gravity material 497 00:24:31,640 --> 00:24:33,970 which is growing and growing in volume 498 00:24:33,970 --> 00:24:36,620 is precisely canceled by the negative energy 499 00:24:36,620 --> 00:24:39,590 of the gravitational field that's filling the region. 500 00:24:39,590 --> 00:24:41,590 So the total energy does remain constant, 501 00:24:41,590 --> 00:24:45,200 as it must, and there's certainly a good possibility 502 00:24:45,200 --> 00:24:46,890 that the total energy is exactly zero. 503 00:24:46,890 --> 00:24:48,869 Because everything that we know of 504 00:24:48,869 --> 00:24:50,660 is at least consistent with the possibility 505 00:24:50,660 --> 00:24:52,950 that these two numbers are exactly 506 00:24:52,950 --> 00:24:55,680 equal to each other or something very close. 507 00:24:55,680 --> 00:24:58,270 Schematically, the picture is that if one thinks 508 00:24:58,270 --> 00:25:01,050 about the total energy of the universe, 509 00:25:01,050 --> 00:25:04,480 it consists of a huge positive amount in the form of matter 510 00:25:04,480 --> 00:25:06,260 and radiation-- the stuff that we see, 511 00:25:06,260 --> 00:25:08,250 the stuff that we normally identify 512 00:25:08,250 --> 00:25:13,260 the energy of-- but there's also a huge negative amount 513 00:25:13,260 --> 00:25:17,100 of energy in the gravitational field that fills the universe. 514 00:25:17,100 --> 00:25:19,350 And as far as we can tell, the sum 515 00:25:19,350 --> 00:25:22,730 is at least consistent with being 0. 516 00:25:22,730 --> 00:25:24,890 In any case, what happens during inflation 517 00:25:24,890 --> 00:25:28,530 is the black bar goes up and the red bar goes down. 518 00:25:28,530 --> 00:25:30,370 And they go up and down by equal amounts. 519 00:25:30,370 --> 00:25:33,960 So certainly what happens during inflation conserves energy, 520 00:25:33,960 --> 00:25:37,940 as anything consistent with the laws of physics that we know of 521 00:25:37,940 --> 00:25:40,750 must conserve energy. 522 00:25:40,750 --> 00:25:43,491 I just remembered I was planning to turn out these blackboard 523 00:25:43,491 --> 00:25:43,990 lights. 524 00:25:48,214 --> 00:25:50,130 It probably makes it a little more comfortable 525 00:25:50,130 --> 00:25:52,590 to watch the screen. 526 00:25:52,590 --> 00:25:53,090 OK. 527 00:25:53,090 --> 00:25:53,875 So, onward. 528 00:25:56,780 --> 00:25:59,740 I want to talk some about the evidence for inflation. 529 00:25:59,740 --> 00:26:02,470 So far I've described what inflation is-- 530 00:26:02,470 --> 00:26:05,460 and I'm sort of done describing what inflation is for today. 531 00:26:05,460 --> 00:26:08,056 As I said, we'll be coming back and talking about all this 532 00:26:08,056 --> 00:26:09,180 during the coming semester. 533 00:26:11,740 --> 00:26:13,770 Now let's move on to discuss some of the reasons 534 00:26:13,770 --> 00:26:16,960 why we think that our universe may very likely have actually 535 00:26:16,960 --> 00:26:19,430 undergone this process called inflation 536 00:26:19,430 --> 00:26:22,070 I was just telling you about. 537 00:26:22,070 --> 00:26:24,330 So there are three things I want to talk about. 538 00:26:24,330 --> 00:26:26,850 The first of which is the large scale uniformity 539 00:26:26,850 --> 00:26:28,200 of the universe. 540 00:26:28,200 --> 00:26:30,440 Which is related to what I told you at the beginning, 541 00:26:30,440 --> 00:26:32,580 that if you look out in different directions 542 00:26:32,580 --> 00:26:35,610 in the universe, it really looks the same in all directions. 543 00:26:35,610 --> 00:26:39,010 And the object that can be measured with the most 544 00:26:39,010 --> 00:26:42,780 precision in terms of how things vary with angle, 545 00:26:42,780 --> 00:26:44,420 is the cosmic background radiation-- 546 00:26:44,420 --> 00:26:46,840 because we can measure it from all directions, 547 00:26:46,840 --> 00:26:49,450 and it's essentially a uniform background. 548 00:26:49,450 --> 00:26:52,530 And when that's been done, what's been found 549 00:26:52,530 --> 00:26:56,190 is that the radiation is uniform to the incredible accuracy 550 00:26:56,190 --> 00:26:59,430 of about one part in 100,000-- which really 551 00:26:59,430 --> 00:27:04,250 is a rather spectacular level of uniformity. 552 00:27:04,250 --> 00:27:08,900 So it means the universe really is rather incredibly uniform. 553 00:27:08,900 --> 00:27:13,540 I might mention one proviso here just to be completely accurate. 554 00:27:13,540 --> 00:27:17,170 When one actually just goes out and measures the radiation, 555 00:27:17,170 --> 00:27:20,530 one finds something-- one finds an asymmetry that's 556 00:27:20,530 --> 00:27:22,340 larger than what I just said. 557 00:27:22,340 --> 00:27:25,400 One finds an asymmetry of about 1 part in 1,000, 558 00:27:25,400 --> 00:27:29,370 with one direction being hotter than the opposite direction. 559 00:27:29,370 --> 00:27:34,300 But that 1 part in 1,000 effect we interpret as our motion 560 00:27:34,300 --> 00:27:37,070 through the cosmic background radiation, which makes it 561 00:27:37,070 --> 00:27:38,890 look hotter in one direction and colder 562 00:27:38,890 --> 00:27:40,840 in the opposite direction. 563 00:27:40,840 --> 00:27:43,560 And the effect of our motion has a very definite angular 564 00:27:43,560 --> 00:27:45,160 pattern. 565 00:27:45,160 --> 00:27:48,030 We have no other way of knowing what our velocity is 566 00:27:48,030 --> 00:27:50,700 relative to the cosmic background radiation. 567 00:27:50,700 --> 00:27:53,255 So we just measure it from this asymmetry, 568 00:27:53,255 --> 00:27:54,130 but we're restricted. 569 00:27:54,130 --> 00:27:55,890 We can't let it account for everything. 570 00:27:55,890 --> 00:27:58,140 Because it has a very different angular form, 571 00:27:58,140 --> 00:28:00,490 we only get to determine one velocity. 572 00:28:00,490 --> 00:28:02,940 And once we determine that, that determines one asymmetry 573 00:28:02,940 --> 00:28:04,700 and you can subtract that out. 574 00:28:04,700 --> 00:28:06,890 And then the residual asymmetries, 575 00:28:06,890 --> 00:28:12,130 the asymmetries that we cannot account for by saying that 576 00:28:12,130 --> 00:28:14,600 the Earth has a certain velocity relative to the cosmic 577 00:28:14,600 --> 00:28:17,780 background radiation, those asymmetries are at the level 578 00:28:17,780 --> 00:28:22,040 of 1 part in 100,000. 579 00:28:22,040 --> 00:28:24,210 And this is 1 part in 100,000 that we attribute 580 00:28:24,210 --> 00:28:26,730 to the universe and not to the motion of the earth. 581 00:28:29,251 --> 00:28:29,750 OK. 582 00:28:29,750 --> 00:28:32,170 So to understand the implications 583 00:28:32,170 --> 00:28:34,700 of this incredible degree of uniformity, 584 00:28:34,700 --> 00:28:36,400 we need to say a little bit about what 585 00:28:36,400 --> 00:28:38,970 we think the history of this cosmic background radiation 586 00:28:38,970 --> 00:28:40,760 was. 587 00:28:40,760 --> 00:28:43,900 And what our theories tell us-- and we'll 588 00:28:43,900 --> 00:28:46,110 be learning about this in detail-- 589 00:28:46,110 --> 00:28:48,720 is that in the early period-- Yes. 590 00:28:48,720 --> 00:28:50,220 AUDIENCE: I'm sorry. 591 00:28:50,220 --> 00:28:51,220 I'm curious. 592 00:28:51,220 --> 00:28:53,220 When they released WMAP and stuff, 593 00:28:53,220 --> 00:28:56,219 did they already subtract out the relativistic effect? 594 00:28:56,219 --> 00:28:58,510 PROFESSOR: Well, the answer is that they analyze things 595 00:28:58,510 --> 00:29:00,960 according to angular patterns and how 596 00:29:00,960 --> 00:29:03,040 they fit different angular patterns. 597 00:29:03,040 --> 00:29:05,427 So in fact, I think they don't even report it with WMAP, 598 00:29:05,427 --> 00:29:07,010 but it would be what they would call L 599 00:29:07,010 --> 00:29:09,280 equals 1, the dipole term. 600 00:29:09,280 --> 00:29:11,940 They analyze the dipole, quadrupole, octupole, et 601 00:29:11,940 --> 00:29:13,506 cetera. 602 00:29:13,506 --> 00:29:15,630 So it really does not contribute at all to anything 603 00:29:15,630 --> 00:29:17,330 except that L equals 1 term, which 604 00:29:17,330 --> 00:29:20,160 is one out of 1,800 things that they measure. 605 00:29:20,160 --> 00:29:22,715 So basically, I think they don't even 606 00:29:22,715 --> 00:29:24,090 bother reporting that one number, 607 00:29:24,090 --> 00:29:25,506 and therefore it's subtracted out. 608 00:29:32,720 --> 00:29:33,220 OK. 609 00:29:33,220 --> 00:29:34,970 Do feel free to ask questions, by the way. 610 00:29:37,818 --> 00:29:39,657 I think it's certainly a small enough class 611 00:29:39,657 --> 00:29:40,490 that we can do that. 612 00:29:43,380 --> 00:29:43,880 OK. 613 00:29:43,880 --> 00:29:46,920 So what I was about to say is that this radiation 614 00:29:46,920 --> 00:29:50,480 during the early period of the universe, when the universe was 615 00:29:50,480 --> 00:29:53,140 a plasma, the radiation was essentially 616 00:29:53,140 --> 00:29:55,050 locked to the matter. 617 00:29:55,050 --> 00:29:58,030 The photons were moving at the speed of light, 618 00:29:58,030 --> 00:30:01,330 but in the plasma there's a very large cross section 619 00:30:01,330 --> 00:30:03,720 for the photons to scatter off of the free electrons 620 00:30:03,720 --> 00:30:05,730 in a plasma. 621 00:30:05,730 --> 00:30:12,240 Which basically means that the photons move with the matter-- 622 00:30:12,240 --> 00:30:14,370 because when they're moving on their own, 623 00:30:14,370 --> 00:30:15,870 they just move a very short distance 624 00:30:15,870 --> 00:30:18,140 and then scatter, and then move in a different direction. 625 00:30:18,140 --> 00:30:19,723 So relative to the matter, the photons 626 00:30:19,723 --> 00:30:22,160 go nowhere during the first 400,000 years 627 00:30:22,160 --> 00:30:24,380 of the history of the universe. 628 00:30:24,380 --> 00:30:26,950 But then at about 400,000 years the universe 629 00:30:26,950 --> 00:30:29,640 cools enough-- this is all according 630 00:30:29,640 --> 00:30:32,420 to our calculations-- the universe cools 631 00:30:32,420 --> 00:30:35,690 enough so that the plasma neutralizes. 632 00:30:35,690 --> 00:30:38,240 And when the plasma neutralizes, it becomes a neutral gas 633 00:30:38,240 --> 00:30:40,730 like the air in this room. 634 00:30:40,730 --> 00:30:44,130 And the air in this room seems completely transparent to us, 635 00:30:44,130 --> 00:30:45,750 and it turns out that actually does 636 00:30:45,750 --> 00:30:48,330 extrapolate to the universe. 637 00:30:48,330 --> 00:30:51,850 The gas that filled the universe after it neutralized really 638 00:30:51,850 --> 00:30:55,920 was transparent, and it means that a typical photon that we 639 00:30:55,920 --> 00:30:59,080 see today in the cosmic background radiation 640 00:30:59,080 --> 00:31:02,440 really has been traveling on a straight line since about 641 00:31:02,440 --> 00:31:05,870 400,000 years after the Big Bang. 642 00:31:05,870 --> 00:31:09,460 Which in turn means that when we look at the cosmic background 643 00:31:09,460 --> 00:31:12,530 radiation, we're essentially seeing 644 00:31:12,530 --> 00:31:16,780 an image of what the universe looked like at 400,000 years 645 00:31:16,780 --> 00:31:19,110 after the Big Bang. 646 00:31:19,110 --> 00:31:21,730 Just as the light traveling from my face to your eyes 647 00:31:21,730 --> 00:31:25,579 gives you an image of what I look like. 648 00:31:25,579 --> 00:31:27,870 So that's what we're seeing-- a picture of the universe 649 00:31:27,870 --> 00:31:30,480 at the age of 400,000 years, and it's 650 00:31:30,480 --> 00:31:36,880 bland-- uniform to 1 part in 100,000. 651 00:31:36,880 --> 00:31:39,970 So the question then is, can we explain 652 00:31:39,970 --> 00:31:42,990 how the universe to be so uniform? 653 00:31:42,990 --> 00:31:48,320 And it turns out that if you-- Well, I should say first of all 654 00:31:48,320 --> 00:31:50,000 that if you're willing to just assume 655 00:31:50,000 --> 00:31:52,980 that the universe started out perfectly uniform to better 656 00:31:52,980 --> 00:31:55,550 than one part in 100,000, that's OK. 657 00:31:55,550 --> 00:31:57,650 Nobody could stop you from doing that. 658 00:31:57,650 --> 00:32:01,270 But if you want to try to explain this uniformity 659 00:32:01,270 --> 00:32:05,440 without assuming that it was there from the beginning, then 660 00:32:05,440 --> 00:32:08,630 within the context of the conventional Big Bang theory, 661 00:32:08,630 --> 00:32:10,400 it's just not possible. 662 00:32:10,400 --> 00:32:15,060 And the reason is that within the evolution equations 663 00:32:15,060 --> 00:32:18,510 of the conventional Big Bang theory, you can calculate-- 664 00:32:18,510 --> 00:32:21,250 and we will calculate later in the course-- 665 00:32:21,250 --> 00:32:24,510 that in order to smooth things out in time for it to look 666 00:32:24,510 --> 00:32:27,530 smooth in the cosmic background radiation, 667 00:32:27,530 --> 00:32:30,050 you have to be able to move around matter and energy 668 00:32:30,050 --> 00:32:33,320 at about 100 times the speed of light. 669 00:32:33,320 --> 00:32:35,000 Or else you just couldn't do it. 670 00:32:35,000 --> 00:32:37,500 And we don't know of anything in physics that happens faster 671 00:32:37,500 --> 00:32:40,054 than the speed of light. 672 00:32:40,054 --> 00:32:42,720 So within physics as we know it, and within the conventional Big 673 00:32:42,720 --> 00:32:46,410 Bang theory, there's no way to explain this uniformity except 674 00:32:46,410 --> 00:32:49,380 to just assume that maybe it was there from the very beginning. 675 00:32:49,380 --> 00:32:51,980 For reasons that we don't know about. 676 00:32:51,980 --> 00:32:56,490 On the other hand, inflation takes care of this very nicely. 677 00:32:56,490 --> 00:33:00,330 What inflation does is it adds this spurt 678 00:33:00,330 --> 00:33:04,910 of exponential expansion to the history of the universe. 679 00:33:04,910 --> 00:33:06,990 And the fact that this exponential expansion 680 00:33:06,990 --> 00:33:10,040 was so humongous means that if you 681 00:33:10,040 --> 00:33:12,270 look at our picture of the universe 682 00:33:12,270 --> 00:33:15,530 before the inflation happened, the universe 683 00:33:15,530 --> 00:33:19,880 would have been vastly smaller than in conventional cosmology 684 00:33:19,880 --> 00:33:24,120 which would not have this exponential spurt of expansion. 685 00:33:24,120 --> 00:33:26,010 So in the inflationary model there 686 00:33:26,010 --> 00:33:29,060 would've been plenty of time for the observed 687 00:33:29,060 --> 00:33:32,230 part of the universe to become uniform before inflation 688 00:33:32,230 --> 00:33:36,002 started-- when it was incredibly tiny. 689 00:33:36,002 --> 00:33:38,460 And then would become uniform just like the air in the room 690 00:33:38,460 --> 00:33:41,312 here tends to spread out and produce a uniform distribution 691 00:33:41,312 --> 00:33:43,270 of air rather than having all the air collected 692 00:33:43,270 --> 00:33:45,830 in one corner. 693 00:33:45,830 --> 00:33:47,320 Once that uniformity is established 694 00:33:47,320 --> 00:33:49,540 on this tiny region, inflation would then 695 00:33:49,540 --> 00:33:51,077 take over and stretch this region 696 00:33:51,077 --> 00:33:52,910 to become large enough to include everything 697 00:33:52,910 --> 00:33:55,390 that we now see, thereby explaining 698 00:33:55,390 --> 00:33:58,560 why everything that we see looks so uniform. 699 00:33:58,560 --> 00:34:01,170 It's a very simple explanation, and it's 700 00:34:01,170 --> 00:34:03,330 only possible with inflation and not 701 00:34:03,330 --> 00:34:05,000 within the conventional Big Bang theory. 702 00:34:08,005 --> 00:34:09,255 So, the inflationary solution. 703 00:34:09,255 --> 00:34:11,250 In inflationary models the universe 704 00:34:11,250 --> 00:34:16,384 begins so small that uniformity is easily established. 705 00:34:16,384 --> 00:34:18,550 Just like the air in the lecture hall-- same analogy 706 00:34:18,550 --> 00:34:22,500 I used-- spreads uniformly to fill the lecture hall. 707 00:34:22,500 --> 00:34:24,250 Then inflation stretches the region 708 00:34:24,250 --> 00:34:26,699 to become large enough to include everything 709 00:34:26,699 --> 00:34:29,441 that we now observe. 710 00:34:29,441 --> 00:34:29,940 OK. 711 00:34:29,940 --> 00:34:31,880 So that's the first of my three pieces 712 00:34:31,880 --> 00:34:33,860 of evidence for inflation. 713 00:34:33,860 --> 00:34:36,545 The second one is something called the flatness problem. 714 00:34:39,100 --> 00:34:45,139 And the question is, why was the early universe so flat? 715 00:34:45,139 --> 00:34:47,449 And the first question maybe is, what am I 716 00:34:47,449 --> 00:34:50,639 talking about when I say the early universe was flat? 717 00:34:50,639 --> 00:34:52,840 One misconception I sometimes find 718 00:34:52,840 --> 00:34:56,242 people getting is that flat often means two dimensional. 719 00:34:56,242 --> 00:34:57,200 That's not what I mean. 720 00:34:57,200 --> 00:34:59,500 It's not flat like a two dimensional pancake. 721 00:34:59,500 --> 00:35:01,190 It's three dimensional. 722 00:35:01,190 --> 00:35:04,670 The flat in this context means Euclidean-- 723 00:35:04,670 --> 00:35:07,870 obeying the axioms of Euclidean geometry-- as opposed 724 00:35:07,870 --> 00:35:10,370 to the non-Euclidean options that 725 00:35:10,370 --> 00:35:13,780 are offered by general relativity. 726 00:35:13,780 --> 00:35:18,190 General relativity allows three dimensional space to be curved. 727 00:35:18,190 --> 00:35:25,014 And if we only consider uniform curvature, which is-- we 728 00:35:25,014 --> 00:35:26,430 don't see any curvature, actually, 729 00:35:26,430 --> 00:35:29,105 but-- We know with better accuracy 730 00:35:29,105 --> 00:35:34,420 that the universe is uniform than we do that it's flat. 731 00:35:34,420 --> 00:35:37,930 So imagine in terms of discussion of cosmology 732 00:35:37,930 --> 00:35:40,470 three possible curvatures for the universe, all of which 733 00:35:40,470 --> 00:35:42,970 would be taken to be uniform. 734 00:35:42,970 --> 00:35:47,300 Three dimensional curved spaces are not easy to visualize, 735 00:35:47,300 --> 00:35:49,670 but all three of these are closely 736 00:35:49,670 --> 00:35:52,140 analogous to two dimensional curved spaces, which 737 00:35:52,140 --> 00:35:54,590 are easy to think about. 738 00:35:54,590 --> 00:35:59,690 One is the closed geometry of the surface of a sphere. 739 00:35:59,690 --> 00:36:01,950 Now the analogy is that the three dimensional universe 740 00:36:01,950 --> 00:36:03,658 would be analogous to the two dimensional 741 00:36:03,658 --> 00:36:05,320 surface of a sphere. 742 00:36:05,320 --> 00:36:08,820 The analogy changes the number of dimensions. 743 00:36:08,820 --> 00:36:10,350 But important things get capped. 744 00:36:10,350 --> 00:36:13,650 Like for example on the surface of a sphere, 745 00:36:13,650 --> 00:36:17,470 you can easily visualize-- and there's even 746 00:36:17,470 --> 00:36:20,660 a picture to show you-- that if you 747 00:36:20,660 --> 00:36:23,100 put a triangle on the surface of a sphere, 748 00:36:23,100 --> 00:36:26,130 the sum of the three angles at the vertices 749 00:36:26,130 --> 00:36:28,740 would be more than 180 degrees. 750 00:36:28,740 --> 00:36:32,100 Unlike the Euclidean case, where it's always 180 degrees. 751 00:36:32,100 --> 00:36:32,600 Question? 752 00:36:32,600 --> 00:36:33,680 AUDIENCE: Yeah. 753 00:36:33,680 --> 00:36:37,330 Is the 3D curving happening in a fourth dimension? 754 00:36:37,330 --> 00:36:39,859 Just like these 2D models assume another dimension? 755 00:36:39,859 --> 00:36:40,900 PROFESSOR: Good question. 756 00:36:40,900 --> 00:36:44,560 The question was, is the 3D curvature 757 00:36:44,560 --> 00:36:48,530 happening in a fourth dimension just like this 2D curvature 758 00:36:48,530 --> 00:36:51,300 is happening in a third dimension? 759 00:36:51,300 --> 00:36:53,820 The answer I guess is yes. 760 00:36:53,820 --> 00:36:57,590 But I should maybe clarify the "just like" part. 761 00:36:57,590 --> 00:37:02,060 The third dimension here from a strictly mathematical point 762 00:37:02,060 --> 00:37:06,050 of view allows us to visualize the sphere in an easy way, 763 00:37:06,050 --> 00:37:08,650 but the geometry of the sphere from the point of view 764 00:37:08,650 --> 00:37:12,030 of people who study differential geometry is a perfectly well 765 00:37:12,030 --> 00:37:15,110 defined two dimensional space without any need 766 00:37:15,110 --> 00:37:17,110 for the third dimension to be there. 767 00:37:17,110 --> 00:37:19,490 The third dimension is really just a crutch for us 768 00:37:19,490 --> 00:37:21,010 to visualize it. 769 00:37:21,010 --> 00:37:23,900 But that same crutch does work in going from three to four. 770 00:37:23,900 --> 00:37:26,940 And in fact when we study the three dimensional curved space 771 00:37:26,940 --> 00:37:30,260 of the closed universe, we will in fact do it exactly that way. 772 00:37:30,260 --> 00:37:34,170 We'll introduce the same crutch, imagine it in four dimensions, 773 00:37:34,170 --> 00:37:36,819 and it will be very closely analogous to the two 774 00:37:36,819 --> 00:37:38,610 dimensional picture that you're looking at. 775 00:37:43,350 --> 00:37:44,460 OK. 776 00:37:44,460 --> 00:37:46,537 So one of the possibilities is a closed geometry 777 00:37:46,537 --> 00:37:48,495 where the sum of the three angles of a triangle 778 00:37:48,495 --> 00:37:51,206 is always bigger than 180 degrees. 779 00:37:51,206 --> 00:37:52,830 Another possibility is something that's 780 00:37:52,830 --> 00:37:55,760 usually described as saddle shaped, 781 00:37:55,760 --> 00:37:58,500 or a space of negative curvature. 782 00:37:58,500 --> 00:38:01,490 And in that case the sum of the three angles-- 783 00:38:01,490 --> 00:38:03,340 they get pinched, and the sum of the angles 784 00:38:03,340 --> 00:38:05,260 is less than 180 degrees. 785 00:38:05,260 --> 00:38:09,240 And only for the flat case is the sum of the three angles 786 00:38:09,240 --> 00:38:13,540 exactly 180 degrees, which is the case of Euclidean geometry. 787 00:38:13,540 --> 00:38:16,220 The geometries on the surfaces of these objects 788 00:38:16,220 --> 00:38:18,530 is non-Euclidean, even though if you 789 00:38:18,530 --> 00:38:20,940 think of the three dimensional geometry of the objects 790 00:38:20,940 --> 00:38:24,060 embedded in three dimensional space, that's still Euclidean. 791 00:38:24,060 --> 00:38:27,080 But the restricted geometry to the two dimensional surfaces 792 00:38:27,080 --> 00:38:30,320 are non-Euclidean there and there, but Euclidean there. 793 00:38:30,320 --> 00:38:33,630 And that's exactly the way it works in general relativity. 794 00:38:33,630 --> 00:38:38,260 There are closed universes with positive curvature and the sum 795 00:38:38,260 --> 00:38:40,970 of angles being more than 180 degrees. 796 00:38:40,970 --> 00:38:43,640 And there are open universes where the sum of three angles 797 00:38:43,640 --> 00:38:45,940 is always less than 180 degrees. 798 00:38:45,940 --> 00:38:47,540 And there's the flat case-- which 799 00:38:47,540 --> 00:38:50,320 is just on the borderline of those two-- 800 00:38:50,320 --> 00:38:52,380 where Euclidean geometry works. 801 00:38:52,380 --> 00:38:54,436 And the point is that in our universe, 802 00:38:54,436 --> 00:38:56,060 Euclidean geometry does work very well. 803 00:38:56,060 --> 00:38:58,100 That's why we all learned it in high school. 804 00:38:58,100 --> 00:38:59,847 And in fact we have very good evidence 805 00:38:59,847 --> 00:39:01,930 that the early universe was rather extraordinarily 806 00:39:01,930 --> 00:39:05,210 close to this flat case of Euclidean geometry. 807 00:39:05,210 --> 00:39:09,520 And that's what we're trying to understand and explain. 808 00:39:09,520 --> 00:39:14,640 According to general relativity this flatness of the geometry 809 00:39:14,640 --> 00:39:17,530 is determined by the mass density. 810 00:39:17,530 --> 00:39:20,820 There's a certain value of the mass density called 811 00:39:20,820 --> 00:39:24,593 the critical density-- which depends on the expansion rate, 812 00:39:24,593 --> 00:39:27,300 by the way, it's not a universal constant of any kind. 813 00:39:27,300 --> 00:39:29,400 But for a given expansion rate one 814 00:39:29,400 --> 00:39:32,180 can calculate a critical density, 815 00:39:32,180 --> 00:39:33,870 and that critical density is the density 816 00:39:33,870 --> 00:39:37,110 which makes the universe flat. 817 00:39:37,110 --> 00:39:43,440 And cosmologists define a number called omega-- capital omega-- 818 00:39:43,440 --> 00:39:45,270 which is just the ratio of the actual mass 819 00:39:45,270 --> 00:39:49,090 density to the critical mass density. 820 00:39:49,090 --> 00:39:51,486 So omega equals 1 says the actual density is 821 00:39:51,486 --> 00:39:52,860 the critical density, which means 822 00:39:52,860 --> 00:39:54,800 the universe would be flat. 823 00:39:54,800 --> 00:40:00,500 Omega bigger than 1 would be a closed universe, and omega 824 00:40:00,500 --> 00:40:02,715 less than 1 would be an open universe. 825 00:40:05,880 --> 00:40:08,680 What's peculiar about the evolution of this omega 826 00:40:08,680 --> 00:40:12,550 quantity is that omega equals 1 as the universe 827 00:40:12,550 --> 00:40:14,970 evolves in conventional cosmology 828 00:40:14,970 --> 00:40:19,590 behaves very much like a pencil balancing on its tip. 829 00:40:19,590 --> 00:40:23,250 It's an unstable equilibrium point. 830 00:40:23,250 --> 00:40:28,190 So in other words, if omega was exactly equal to 1 831 00:40:28,190 --> 00:40:32,080 in the early universe, it would remain exactly equal to 1. 832 00:40:32,080 --> 00:40:35,540 Just like a pencil that's perfectly balanced on its tip 833 00:40:35,540 --> 00:40:38,460 would not know which way to fall and would in principle stay 834 00:40:38,460 --> 00:40:39,120 there forever. 835 00:40:39,120 --> 00:40:41,170 At least with classical mechanics. 836 00:40:41,170 --> 00:40:44,500 We won't include quantum mechanics for our pencil. 837 00:40:44,500 --> 00:40:49,440 Classical pencil that we're using for the analogy. 838 00:40:49,440 --> 00:40:53,470 But if the pencil leans just a tiny bit in any direction, 839 00:40:53,470 --> 00:40:57,050 it will rapidly start to fall over in that direction. 840 00:40:57,050 --> 00:40:59,680 And similarly if omega in the early universe 841 00:40:59,680 --> 00:41:01,850 was just slightly greater than 1, 842 00:41:01,850 --> 00:41:04,621 it would rapidly rise towards infinity. 843 00:41:04,621 --> 00:41:05,870 And this is a closed universe. 844 00:41:05,870 --> 00:41:07,786 Infinity really means the universe has reached 845 00:41:07,786 --> 00:41:11,160 its maximum size, and it turns around and collapses. 846 00:41:11,160 --> 00:41:13,770 And if omega was slightly less than 1, 847 00:41:13,770 --> 00:41:15,204 it would rapidly dribble off to 0, 848 00:41:15,204 --> 00:41:16,870 and the universe would just become empty 849 00:41:16,870 --> 00:41:19,930 as it rapidly expands. 850 00:41:19,930 --> 00:41:23,735 So the only way for omega to be close to 1 today-- 851 00:41:23,735 --> 00:41:25,870 and as far as we can tell, omega is consistent 852 00:41:25,870 --> 00:41:28,720 with 1 today-- the only way that can happen 853 00:41:28,720 --> 00:41:32,120 is if omega started out unbelievably close to 1. 854 00:41:32,120 --> 00:41:34,740 Unless it's this pencil that's been standing there 855 00:41:34,740 --> 00:41:40,330 for 14 billion years and hasn't fallen over yet. 856 00:41:40,330 --> 00:41:44,590 Numerically, for omega to be somewhere in the allowed range 857 00:41:44,590 --> 00:41:47,600 today, which is very close to 1, it 858 00:41:47,600 --> 00:41:51,080 means that omega at one second after the Big Bang 859 00:41:51,080 --> 00:41:53,930 had to be equal to 1 to the incredible accuracy of 15 860 00:41:53,930 --> 00:41:56,930 decimal places. 861 00:41:56,930 --> 00:41:58,860 Which makes the value of the mass density 862 00:41:58,860 --> 00:42:01,379 of the universe at one second after the Big Bang probably 863 00:42:01,379 --> 00:42:03,420 the most accurate number that we know in physics. 864 00:42:03,420 --> 00:42:05,430 Since we really know it to 15 decimal places. 865 00:42:05,430 --> 00:42:06,805 So if it wasn't in that range, it 866 00:42:06,805 --> 00:42:09,390 wouldn't be in the [? lab manuals ?] today. 867 00:42:09,390 --> 00:42:11,630 We have this amplification effect 868 00:42:11,630 --> 00:42:14,450 of the evolution of the universe. 869 00:42:14,450 --> 00:42:17,700 So the question is, how did this happen? 870 00:42:17,700 --> 00:42:21,420 In conventional Big Bang theory, the initial value of omega 871 00:42:21,420 --> 00:42:23,830 could have been anything, logically. 872 00:42:23,830 --> 00:42:25,720 To be consistent with what we now observe it 873 00:42:25,720 --> 00:42:28,570 has to be within this incredibly narrow range, 874 00:42:28,570 --> 00:42:30,590 but there's nothing in the theory which 875 00:42:30,590 --> 00:42:33,220 causes it to be in that narrow range. 876 00:42:33,220 --> 00:42:35,430 So the question is, why did omega 877 00:42:35,430 --> 00:42:39,080 start out so incredibly close to 1? 878 00:42:39,080 --> 00:42:43,420 Like the earlier problem about homogeneity, 879 00:42:43,420 --> 00:42:47,640 if you want to just assume that it started out-- exactly 880 00:42:47,640 --> 00:42:51,890 like, it had to be-- at omega equals 1, you could do that. 881 00:42:51,890 --> 00:42:54,290 But if you want to have any dynamical explanation for how 882 00:42:54,290 --> 00:42:56,340 it got to be that way, there's really 883 00:42:56,340 --> 00:42:59,150 nothing in conventional cosmology which does it. 884 00:42:59,150 --> 00:43:01,670 But in fact, inflation does. 885 00:43:01,670 --> 00:43:07,120 In the inflationary model we've changed the evolution of omega 886 00:43:07,120 --> 00:43:10,055 because we've turned gravity into a repulsive force instead 887 00:43:10,055 --> 00:43:13,400 of an attractive force, and that changes the way omega evolves. 888 00:43:13,400 --> 00:43:15,880 And it turns out that during inflation, omega 889 00:43:15,880 --> 00:43:18,670 is not driven away from 1-- as it 890 00:43:18,670 --> 00:43:21,770 is during the entire rest of the history of the universe-- 891 00:43:21,770 --> 00:43:24,640 but rather during inflation omega is driven rapidly 892 00:43:24,640 --> 00:43:27,970 towards 1, exponentially fast, even. 893 00:43:27,970 --> 00:43:29,680 So with the amount of inflation that we 894 00:43:29,680 --> 00:43:36,080 talked about-- inflation by a factor of 10 to the 28 or so-- 895 00:43:36,080 --> 00:43:40,440 that's enough so that the value of omega before inflation 896 00:43:40,440 --> 00:43:42,720 is not very much constrained. 897 00:43:42,720 --> 00:43:45,505 Omega could have started out before inflation not being 1, 898 00:43:45,505 --> 00:43:50,650 but being 2 or 10 or 1/10 or 100 or 1/100. 899 00:43:50,650 --> 00:43:53,760 The further away you start omega from 1, 900 00:43:53,760 --> 00:43:57,697 the more inflation you need to drive it to 1 sufficiently. 901 00:43:57,697 --> 00:43:59,280 But you don't need much more inflation 902 00:43:59,280 --> 00:44:01,410 to make it significantly far away from 1 903 00:44:01,410 --> 00:44:05,180 because of this fact the inflation drives omega 904 00:44:05,180 --> 00:44:06,360 to 1 exponentially. 905 00:44:06,360 --> 00:44:09,290 Which really means it's a very powerful force driving 906 00:44:09,290 --> 00:44:10,400 omega to 1. 907 00:44:10,400 --> 00:44:12,170 And giving us a very simple, therefore, 908 00:44:12,170 --> 00:44:15,830 explanation for why omega in the early universe 909 00:44:15,830 --> 00:44:18,310 appears to have been extraordinarily close to 1. 910 00:44:21,360 --> 00:44:26,810 So I think that's-- Oh, I have a few more things to say. 911 00:44:26,810 --> 00:44:29,400 There's actually a prediction that comes out of this, 912 00:44:29,400 --> 00:44:33,830 because this tendency of inflation to drive omega to 1 913 00:44:33,830 --> 00:44:36,740 is so strong, that you expect that omega really 914 00:44:36,740 --> 00:44:38,450 should be 1 today. 915 00:44:38,450 --> 00:44:42,550 Or to within measurable accuracy. 916 00:44:42,550 --> 00:44:44,270 You could arrange inflationary models 917 00:44:44,270 --> 00:44:47,000 where it's say, 0.2-- which is what people used 918 00:44:47,000 --> 00:44:50,000 to think it was-- but in order to do that, you have to arrange 919 00:44:50,000 --> 00:44:52,000 for inflation to end at just the right time 920 00:44:52,000 --> 00:44:55,470 before it makes it closer. 921 00:44:55,470 --> 00:44:58,990 Because every e-fold drives it another factor of 10 closer. 922 00:44:58,990 --> 00:45:01,330 So it's very rapid effect. 923 00:45:01,330 --> 00:45:05,450 So if you don't fine tune things very carefully, most 924 00:45:05,450 --> 00:45:08,460 any inflationary model will drive omega so close to 1 925 00:45:08,460 --> 00:45:12,020 that today we would see it as 1. 926 00:45:12,020 --> 00:45:15,070 That did not used to appear to be the case. 927 00:45:15,070 --> 00:45:20,050 Before 1998 astronomers were pretty sure 928 00:45:20,050 --> 00:45:24,355 that omega was only 0.2 or 0.3, while inflation seemed 929 00:45:24,355 --> 00:45:26,480 to have a pretty clear prediction that omega should 930 00:45:26,480 --> 00:45:28,340 be 1. 931 00:45:28,340 --> 00:45:32,260 This personally I found rather uncomfortable, because it meant 932 00:45:32,260 --> 00:45:34,520 whenever I had dinner with astronomers, 933 00:45:34,520 --> 00:45:36,820 they would always sort of snidely talk about 934 00:45:36,820 --> 00:45:38,870 how inflation was a pretty theory, 935 00:45:38,870 --> 00:45:41,370 but it couldn't be right because omega was 0.2, 936 00:45:41,370 --> 00:45:43,520 and inflation was predicting omega is 1. 937 00:45:43,520 --> 00:45:46,590 And it just didn't fit. 938 00:45:46,590 --> 00:45:50,639 Things changed a lot in 1998, and now the best number we 939 00:45:50,639 --> 00:45:53,055 have-- which comes from the Planck satellite combined with 940 00:45:53,055 --> 00:45:55,410 a few other measurements, actually-- 941 00:45:55,410 --> 00:46:00,890 is that now the observational number for omega is 1.0010, 942 00:46:00,890 --> 00:46:04,510 plus or minus 0.0065. 943 00:46:04,510 --> 00:46:06,990 So the 0.0065 is the important thing. 944 00:46:06,990 --> 00:46:09,190 This is very, very close to 1, but the error bars 945 00:46:09,190 --> 00:46:11,200 are bigger than this difference. 946 00:46:11,200 --> 00:46:14,850 So it really means to about a half a percent or maybe 1%, 947 00:46:14,850 --> 00:46:17,880 we know today that omega is 1, which 948 00:46:17,880 --> 00:46:20,030 is what inflation would predict. 949 00:46:20,030 --> 00:46:22,045 That it should essentially be exactly 1 today. 950 00:46:25,690 --> 00:46:28,850 The new ingredient that made all this possible, 951 00:46:28,850 --> 00:46:32,960 that drove-- changed the measurement of omega 952 00:46:32,960 --> 00:46:35,950 from 0.2 to 1 is a new ingredient 953 00:46:35,950 --> 00:46:38,540 to the energy budget of the universe, the discovery of what 954 00:46:38,540 --> 00:46:39,485 we call dark energy. 955 00:46:39,485 --> 00:46:41,360 And we'll be learning a lot about dark energy 956 00:46:41,360 --> 00:46:44,420 during the course of the term. 957 00:46:44,420 --> 00:46:48,120 The real discovery in 1998 was that the universe is not 958 00:46:48,120 --> 00:46:50,880 slowing down under the influence of gravity 959 00:46:50,880 --> 00:46:54,177 as had been expected until that time, but rather the universe 960 00:46:54,177 --> 00:46:55,218 actually is accelerating. 961 00:46:58,050 --> 00:47:03,300 And this acceleration has to be attributed to something. 962 00:47:03,300 --> 00:47:06,750 The stuff that it's attributed to is called the dark energy. 963 00:47:06,750 --> 00:47:09,150 And even though there's considerable ignorance 964 00:47:09,150 --> 00:47:11,509 of what exactly this dark energy is, 965 00:47:11,509 --> 00:47:13,050 we can still calculate how much of it 966 00:47:13,050 --> 00:47:16,260 there's got to be in order to produce the acceleration that's 967 00:47:16,260 --> 00:47:17,160 seen. 968 00:47:17,160 --> 00:47:19,300 And when all that is put together, 969 00:47:19,300 --> 00:47:23,520 you get this number, which is so much nicer for inflation 970 00:47:23,520 --> 00:47:25,271 than the previous number. 971 00:47:25,271 --> 00:47:25,770 Yes. 972 00:47:25,770 --> 00:47:27,250 AUDIENCE: So, was the accelerating universe 973 00:47:27,250 --> 00:47:29,840 like the missing factor which they-- gave a wrong assumption 974 00:47:29,840 --> 00:47:32,200 which made them think that omega was 0.2 or 0.3? 975 00:47:32,200 --> 00:47:33,450 PROFESSOR: Yeah, that's right. 976 00:47:33,450 --> 00:47:34,950 It was entirely because they did not 977 00:47:34,950 --> 00:47:37,210 know about the acceleration at that time. 978 00:47:37,210 --> 00:47:41,090 They in fact were accurately measuring the stuff 979 00:47:41,090 --> 00:47:43,470 that they were looking at. 980 00:47:43,470 --> 00:47:46,320 And that does only add up to 0.2 or 0.3. 981 00:47:46,320 --> 00:47:49,040 And this new ingredient, the dark energy, 982 00:47:49,040 --> 00:47:51,660 which we only know about through the acceleration, 983 00:47:51,660 --> 00:47:53,970 is what makes the difference. 984 00:47:53,970 --> 00:47:54,470 Yes. 985 00:47:54,470 --> 00:47:56,378 AUDIENCE: And that data that they were measuring 986 00:47:56,378 --> 00:47:58,169 is really just sort of the integrated stuff 987 00:47:58,169 --> 00:48:00,200 in the universe that we see through telescopes? 988 00:48:00,200 --> 00:48:01,870 Very straight-forward in that way? 989 00:48:01,870 --> 00:48:02,870 PROFESSOR: That's right. 990 00:48:02,870 --> 00:48:04,500 Including dark matter. 991 00:48:04,500 --> 00:48:06,700 So it's not everything that we actually see. 992 00:48:06,700 --> 00:48:08,860 There's also-- not going into it here, 993 00:48:08,860 --> 00:48:11,370 but we will later in the course-- there is also stuff 994 00:48:11,370 --> 00:48:13,760 called dark matter, which is different from dark energy. 995 00:48:13,760 --> 00:48:15,260 Even though matter and energy are supposed to be the same, 996 00:48:15,260 --> 00:48:17,430 they are different in this context. 997 00:48:17,430 --> 00:48:19,540 And dark matter is matter that we infer 998 00:48:19,540 --> 00:48:22,550 exists due to its effect on other matter. 999 00:48:22,550 --> 00:48:26,064 So by looking, for example, at how fast galaxies rotate, 1000 00:48:26,064 --> 00:48:27,480 you can figure out how much matter 1001 00:48:27,480 --> 00:48:28,938 there must be inside those galaxies 1002 00:48:28,938 --> 00:48:32,294 to allow those orbits to be stable. 1003 00:48:32,294 --> 00:48:34,710 And that's significantly more matter than we actually see. 1004 00:48:34,710 --> 00:48:39,410 And that unseen matter is called the dark matter, 1005 00:48:39,410 --> 00:48:42,080 and that was added into the 0.2 or 0.3. 1006 00:48:42,080 --> 00:48:48,600 The visible matter is only about 0.04. 1007 00:48:48,600 --> 00:48:49,850 OK. 1008 00:48:49,850 --> 00:48:52,260 So, so much for the flatness problem. 1009 00:48:52,260 --> 00:48:57,290 Next item I want talk about is the small scale nonuniformity 1010 00:48:57,290 --> 00:48:58,284 of the universe. 1011 00:48:58,284 --> 00:48:59,700 On the largest scale, the universe 1012 00:48:59,700 --> 00:49:03,690 is incredibly uniform-- one part in 100,000-- but on smaller 1013 00:49:03,690 --> 00:49:07,370 scales, the universe today is incredibly lumpy. 1014 00:49:07,370 --> 00:49:09,750 The earth is a big lump in the mass density 1015 00:49:09,750 --> 00:49:11,850 distribution of the universe. 1016 00:49:11,850 --> 00:49:14,920 The earth is in fact about 10 to the 30 times 1017 00:49:14,920 --> 00:49:18,630 denser than the average matter density in the universe. 1018 00:49:18,630 --> 00:49:21,150 It's an unbelievably significant lump. 1019 00:49:23,790 --> 00:49:26,100 And the question is, how did these lumps form? 1020 00:49:26,100 --> 00:49:28,370 Where did they come from? 1021 00:49:28,370 --> 00:49:32,110 We are confident that these lumps evolved 1022 00:49:32,110 --> 00:49:34,090 from the very minor perturbations 1023 00:49:34,090 --> 00:49:36,221 that we see in the early universe, 1024 00:49:36,221 --> 00:49:38,470 that we see most clearly through the cosmic background 1025 00:49:38,470 --> 00:49:39,970 radiation. 1026 00:49:39,970 --> 00:49:44,060 The early universe we believe was uniform in its mass density 1027 00:49:44,060 --> 00:49:46,960 to about one part in 100,000. 1028 00:49:46,960 --> 00:49:49,237 But at the level of one part in 100,000, 1029 00:49:49,237 --> 00:49:51,320 we actually see in the cosmic background radiation 1030 00:49:51,320 --> 00:49:54,790 that there are nonuniformities. 1031 00:49:54,790 --> 00:49:58,580 And things like the Earth form because 1032 00:49:58,580 --> 00:50:03,350 these small nonuniformities in the mass density 1033 00:50:03,350 --> 00:50:05,660 are gravitationally unstable. 1034 00:50:05,660 --> 00:50:09,330 In regions where there's a slight excess of matter, 1035 00:50:09,330 --> 00:50:12,440 that excess of matter produces a gravitational field 1036 00:50:12,440 --> 00:50:15,000 pulling more matter into those regions, 1037 00:50:15,000 --> 00:50:17,450 producing a still stronger gravitational field pulling 1038 00:50:17,450 --> 00:50:19,200 in more matter. 1039 00:50:19,200 --> 00:50:22,450 And the system is unstable, and it forms complicated lumps 1040 00:50:22,450 --> 00:50:25,530 which are galaxies, stars, planets, et cetera. 1041 00:50:25,530 --> 00:50:27,020 And that's a complicated story. 1042 00:50:27,020 --> 00:50:32,600 But it all starts from these very faint nonuniformities that 1043 00:50:32,600 --> 00:50:35,275 existed, we believe, shortly after the Big Bang. 1044 00:50:35,275 --> 00:50:37,650 And we see these nonuniformities in the cosmic background 1045 00:50:37,650 --> 00:50:39,970 radiation, and measuring them tells us 1046 00:50:39,970 --> 00:50:43,950 a lot about the conditions of the universe 1047 00:50:43,950 --> 00:50:45,630 then, and allows us to build theories 1048 00:50:45,630 --> 00:50:48,090 of how the universe got to be that way. 1049 00:50:48,090 --> 00:50:52,240 And that's what these satellites like COBE, WMAP, and Planck 1050 00:50:52,240 --> 00:50:54,840 are all about-- measuring these nonuniformities 1051 00:50:54,840 --> 00:50:56,325 to rather extraordinary accuracy. 1052 00:50:59,200 --> 00:51:01,060 Inflation has an answer to the riddle 1053 00:51:01,060 --> 00:51:03,831 of where the nonuniformities came from. 1054 00:51:03,831 --> 00:51:05,330 In the conventional Big Bang theory, 1055 00:51:05,330 --> 00:51:06,880 there was really just no explanation. 1056 00:51:06,880 --> 00:51:10,340 People just assumed they were there and put them in by hand, 1057 00:51:10,340 --> 00:51:13,890 but there was no theory of what might have created them. 1058 00:51:13,890 --> 00:51:16,620 In the context of inflationary models 1059 00:51:16,620 --> 00:51:19,920 where all the matter really is being created by the inflation, 1060 00:51:19,920 --> 00:51:23,970 the nonuniformities are also controlled by that inflation, 1061 00:51:23,970 --> 00:51:29,380 and where nonuniformities come from is quantum effects. 1062 00:51:29,380 --> 00:51:31,920 It's a little hard to believe that quantum effects could 1063 00:51:31,920 --> 00:51:37,000 be important for the large scale structure of the universe. 1064 00:51:37,000 --> 00:51:39,134 The Andromeda galaxy doesn't look 1065 00:51:39,134 --> 00:51:40,550 like it's something that should be 1066 00:51:40,550 --> 00:51:43,740 thought of as a quantum fluctuation. 1067 00:51:43,740 --> 00:51:47,600 But when one pursues this theory quantitatively, 1068 00:51:47,600 --> 00:51:50,600 it actually does work very well. 1069 00:51:50,600 --> 00:51:54,440 The theory is that the ripples that we 1070 00:51:54,440 --> 00:51:56,660 see in the cosmic background radiation 1071 00:51:56,660 --> 00:52:00,060 really were purely the consequence of quantum theory-- 1072 00:52:00,060 --> 00:52:03,300 basically the uncertainty principle of quantum theory, 1073 00:52:03,300 --> 00:52:06,580 which says that it's just impossible to have something 1074 00:52:06,580 --> 00:52:08,190 that's completely uniform. 1075 00:52:08,190 --> 00:52:11,124 It's not consistent with the uncertainty principle. 1076 00:52:11,124 --> 00:52:13,540 And when one puts in the basic ideas of quantum mechanics, 1077 00:52:13,540 --> 00:52:18,170 we can actually calculate properties of these ripples. 1078 00:52:18,170 --> 00:52:21,420 It turns out that we would need to know 1079 00:52:21,420 --> 00:52:25,195 more about the physics of very high energy-- 1080 00:52:25,195 --> 00:52:27,920 the physics that was relevant during the period 1081 00:52:27,920 --> 00:52:29,950 of inflation-- to be able to predict 1082 00:52:29,950 --> 00:52:32,510 the actual amplitude of these ripples. 1083 00:52:32,510 --> 00:52:34,695 So we cannot predict the amplitude. 1084 00:52:34,695 --> 00:52:36,320 In principle, inflation would allow you 1085 00:52:36,320 --> 00:52:39,110 to if you knew enough about the underlying particle physics, 1086 00:52:39,110 --> 00:52:40,910 but we don't know that much. 1087 00:52:40,910 --> 00:52:43,900 So in practice we cannot predict the amplitude. 1088 00:52:43,900 --> 00:52:47,140 But inflationary models make a very clear prediction 1089 00:52:47,140 --> 00:52:50,060 for the spectrum of these fluctuations. 1090 00:52:50,060 --> 00:52:52,150 And by that I mean how the intensity varies 1091 00:52:52,150 --> 00:52:53,550 with wavelength. 1092 00:52:53,550 --> 00:52:55,410 So the spectrum really means the same thing 1093 00:52:55,410 --> 00:52:56,720 as it would mean for sound, except you 1094 00:52:56,720 --> 00:52:58,845 should think about wavelength rather than frequency 1095 00:52:58,845 --> 00:53:02,230 because these waves don't really oscillate. 1096 00:53:02,230 --> 00:53:04,830 But they do have wavelengths just like sound waves have 1097 00:53:04,830 --> 00:53:07,090 wavelengths, and if you talk about the intensity 1098 00:53:07,090 --> 00:53:09,150 versus wavelengths, this idea of a spectrum 1099 00:53:09,150 --> 00:53:10,600 is really the same as what you'll 1100 00:53:10,600 --> 00:53:12,830 be talking about with sound. 1101 00:53:12,830 --> 00:53:16,000 And you can measure it. 1102 00:53:16,000 --> 00:53:17,780 This is not quite the latest measurements, 1103 00:53:17,780 --> 00:53:20,120 but it's the latest measurements that I have graphed. 1104 00:53:20,120 --> 00:53:23,550 The red line is the theoretical prediction. 1105 00:53:23,550 --> 00:53:26,060 The black dots are the measurements. 1106 00:53:26,060 --> 00:53:29,275 This goes through the seven year WMAP data. 1107 00:53:29,275 --> 00:53:30,900 We have a little Eureka guy to tell you 1108 00:53:30,900 --> 00:53:33,630 how happy I am about this curve. 1109 00:53:33,630 --> 00:53:38,310 And I also have graphs of what other ideas would predict. 1110 00:53:38,310 --> 00:53:41,170 For a while, for example, people took very seriously the idea 1111 00:53:41,170 --> 00:53:43,850 that the randomness that we see in the universe-- 1112 00:53:43,850 --> 00:53:45,870 these fluctuations-- may have been caused 1113 00:53:45,870 --> 00:53:47,400 by the random formation of things 1114 00:53:47,400 --> 00:53:49,390 called cosmic strings that would form 1115 00:53:49,390 --> 00:53:52,030 in phase transitions in the early universe. 1116 00:53:52,030 --> 00:53:54,370 That was certainly a viable idea in its day, 1117 00:53:54,370 --> 00:53:55,753 but once this curve got measured, 1118 00:53:55,753 --> 00:53:57,586 the cosmic strings were predicting something 1119 00:53:57,586 --> 00:54:00,690 that looked like that, which is nothing at all like that curve. 1120 00:54:00,690 --> 00:54:03,780 And they have since been therefore excluded 1121 00:54:03,780 --> 00:54:09,374 as being the source of density fluctuations in the universe. 1122 00:54:09,374 --> 00:54:11,040 And various other models are shown here. 1123 00:54:11,040 --> 00:54:14,220 I don't think I'll take the time to go into, because there are 1124 00:54:14,220 --> 00:54:16,430 other things I want to talk about. 1125 00:54:16,430 --> 00:54:18,140 But anyway, marvelous success. 1126 00:54:18,140 --> 00:54:19,570 This is actually the latest data. 1127 00:54:19,570 --> 00:54:22,480 This is the Planck data that was released last March. 1128 00:54:22,480 --> 00:54:24,970 I don't have it plotted on the same scale, 1129 00:54:24,970 --> 00:54:27,010 but again you see a theoretical curve 1130 00:54:27,010 --> 00:54:30,630 based on inflation and dots that show 1131 00:54:30,630 --> 00:54:33,710 the data with little tiny error bars. 1132 00:54:33,710 --> 00:54:35,930 But absolutely gorgeous fit. 1133 00:54:35,930 --> 00:54:36,828 Yes. 1134 00:54:36,828 --> 00:54:38,953 AUDIENCE: What happened to your theory of inflation 1135 00:54:38,953 --> 00:54:42,306 after they discovered dark energy? 1136 00:54:42,306 --> 00:54:43,810 Did it change significantly? 1137 00:54:43,810 --> 00:54:44,600 PROFESSOR: Did the theory change? 1138 00:54:44,600 --> 00:54:46,306 AUDIENCE: Or like, in the last graph 1139 00:54:46,306 --> 00:54:48,234 there was a different curve. 1140 00:54:50,367 --> 00:54:52,450 PROFESSOR: Well it's plotted on a different scale, 1141 00:54:52,450 --> 00:54:56,220 but this actually is pretty much the same curve as that curve. 1142 00:54:56,220 --> 00:54:57,220 Although you can't tell. 1143 00:54:57,220 --> 00:54:57,886 AUDIENCE: Sorry. 1144 00:54:57,886 --> 00:54:59,040 PROFESSOR: Oh. 1145 00:54:59,040 --> 00:55:01,310 Oh, inflation without dark energy, for example. 1146 00:55:05,502 --> 00:55:07,710 I think it's not so much that the theory of inflation 1147 00:55:07,710 --> 00:55:09,490 changed between these two curves, 1148 00:55:09,490 --> 00:55:11,730 but the curve you actually see today 1149 00:55:11,730 --> 00:55:15,160 is the result of what things looked like immediately 1150 00:55:15,160 --> 00:55:18,635 after inflation combined with the evolution that took place 1151 00:55:18,635 --> 00:55:19,144 since then. 1152 00:55:19,144 --> 00:55:20,560 And it's really the evolution that 1153 00:55:20,560 --> 00:55:22,740 took place since then that makes a big difference 1154 00:55:22,740 --> 00:55:26,060 between this inflationary curve and the other inflationary 1155 00:55:26,060 --> 00:55:27,540 curve. 1156 00:55:27,540 --> 00:55:29,980 So inflation did not have to change very much at all. 1157 00:55:29,980 --> 00:55:33,132 It really did not. 1158 00:55:33,132 --> 00:55:34,590 But of course it looks a lot better 1159 00:55:34,590 --> 00:55:37,910 after dark energy was discovered because the mass density came 1160 00:55:37,910 --> 00:55:40,520 out right, and gradually we also got more and more data 1161 00:55:40,520 --> 00:55:42,900 about these fluctuations which just fit beautifully 1162 00:55:42,900 --> 00:55:44,150 with what inflation predicts. 1163 00:55:48,400 --> 00:55:48,980 OK. 1164 00:55:48,980 --> 00:55:53,390 I want to now launch into the idea of the multiverse. 1165 00:55:53,390 --> 00:55:56,170 And I guess I'll try to go through this quickly so that we 1166 00:55:56,170 --> 00:55:56,750 can finish. 1167 00:55:58,839 --> 00:56:00,880 We're not going try to understand all the details 1168 00:56:00,880 --> 00:56:04,020 anyway, so I'll talk about fewer of them 1169 00:56:04,020 --> 00:56:06,554 for the remaining 10 minutes of the class. 1170 00:56:06,554 --> 00:56:08,720 But I'd like to say a little bit about how inflation 1171 00:56:08,720 --> 00:56:09,950 leads to the idea of a multiverse. 1172 00:56:09,950 --> 00:56:12,491 Of course we'll come back to it at the very end of the class, 1173 00:56:12,491 --> 00:56:16,205 and it's certainly an exciting, I think, aspect of inflation. 1174 00:56:19,320 --> 00:56:21,700 The repulsive gravity material that drives the inflation 1175 00:56:21,700 --> 00:56:23,520 is metastable, as we said. 1176 00:56:23,520 --> 00:56:25,420 So it decays. 1177 00:56:25,420 --> 00:56:27,610 And that means that if you sit in one place 1178 00:56:27,610 --> 00:56:29,417 and ask where inflation is happening, 1179 00:56:29,417 --> 00:56:31,750 and ask what's the probability that it's still happening 1180 00:56:31,750 --> 00:56:33,700 a little bit later, that probability 1181 00:56:33,700 --> 00:56:36,970 decreases exponentially-- drops by a factor of two 1182 00:56:36,970 --> 00:56:40,300 every doubling, every half life. 1183 00:56:40,300 --> 00:56:45,110 But at the same time, the volume of any region that's inflating 1184 00:56:45,110 --> 00:56:50,410 is also growing exponentially, growing due to the inflation. 1185 00:56:50,410 --> 00:56:54,310 And in fact in any reasonable inflationary model 1186 00:56:54,310 --> 00:56:58,840 the growth rate is vastly faster than the decay rate. 1187 00:56:58,840 --> 00:57:02,530 So if you look at the volume that's 1188 00:57:02,530 --> 00:57:05,660 inflating, if you wait for a half life, 1189 00:57:05,660 --> 00:57:08,180 indeed half of that volume will no longer 1190 00:57:08,180 --> 00:57:11,160 be inflating-- by the definition of a half life. 1191 00:57:11,160 --> 00:57:13,210 But the half that remains will be vastly larger 1192 00:57:13,210 --> 00:57:14,590 than what you started with. 1193 00:57:14,590 --> 00:57:16,110 That's the catch. 1194 00:57:16,110 --> 00:57:17,920 And that's a very peculiar situation 1195 00:57:17,920 --> 00:57:20,880 because it doesn't seem to show any end. 1196 00:57:20,880 --> 00:57:23,870 The volume that's inflating just gets bigger and bigger 1197 00:57:23,870 --> 00:57:28,270 even while it's decaying, because the expansion is faster 1198 00:57:28,270 --> 00:57:30,090 than the decay. 1199 00:57:30,090 --> 00:57:34,230 And that's what leads to this phenomena of eternal inflation. 1200 00:57:34,230 --> 00:57:36,490 The volume that is inflating increases with time, 1201 00:57:36,490 --> 00:57:40,760 even though the inflating material is decaying. 1202 00:57:40,760 --> 00:57:44,260 And that leads to what we call eternal inflation. 1203 00:57:44,260 --> 00:57:46,500 The word "eternal" is being used slightly loosely 1204 00:57:46,500 --> 00:57:49,099 because eternal really means forever. 1205 00:57:49,099 --> 00:57:51,390 This is forever into the future, as far as we can tell, 1206 00:57:51,390 --> 00:57:53,550 but it's not forever into the past. 1207 00:57:53,550 --> 00:57:56,290 Inflation would still start at some finite time here, 1208 00:57:56,290 --> 00:58:00,180 but then once it starts, it goes on forever. 1209 00:58:00,180 --> 00:58:05,060 And whenever a piece of this inflating region 1210 00:58:05,060 --> 00:58:07,360 undergoes a transition and becomes normal, 1211 00:58:07,360 --> 00:58:09,530 that locally looks like a Big Bang. 1212 00:58:09,530 --> 00:58:13,430 And our Big Bang would be one of these local events, 1213 00:58:13,430 --> 00:58:17,810 and the universe formed by any one of these local events 1214 00:58:17,810 --> 00:58:21,270 where the inflating region decays 1215 00:58:21,270 --> 00:58:23,207 would be called a pocket universe. 1216 00:58:23,207 --> 00:58:25,290 Pocket just to suggest that there are many of them 1217 00:58:25,290 --> 00:58:27,220 in the overall scale of this multiverse. 1218 00:58:27,220 --> 00:58:29,230 They are in some sense small, even though they'd 1219 00:58:29,230 --> 00:58:31,100 be as big as the universe that we live in. 1220 00:58:31,100 --> 00:58:35,710 And our universe would be one of these pocket universes. 1221 00:58:35,710 --> 00:58:37,480 So instead of one universe, inflation 1222 00:58:37,480 --> 00:58:39,650 produces an infinite number, which 1223 00:58:39,650 --> 00:58:42,257 is what we call multiverse. 1224 00:58:42,257 --> 00:58:44,090 I might just say the word multiverse is also 1225 00:58:44,090 --> 00:58:47,220 used in other contexts and another theories, 1226 00:58:47,220 --> 00:58:50,170 but inflation, I think, is probably the most plausible way 1227 00:58:50,170 --> 00:58:52,190 of getting a multiverse, and it's 1228 00:58:52,190 --> 00:58:53,720 what most cosmologists are talking 1229 00:58:53,720 --> 00:58:55,520 about when they talk about a multiverse. 1230 00:58:59,310 --> 00:58:59,810 OK. 1231 00:58:59,810 --> 00:59:03,460 Now how does dark energy fit in here? 1232 00:59:03,460 --> 00:59:07,120 It plays a very important role in our understanding. 1233 00:59:07,120 --> 00:59:10,080 To review, in 1998 several groups-- 1234 00:59:10,080 --> 00:59:13,740 two groups of astronomers discovered independently 1235 00:59:13,740 --> 00:59:17,180 that the universe is now accelerating, 1236 00:59:17,180 --> 00:59:19,360 and our understanding is that the universe has 1237 00:59:19,360 --> 00:59:23,230 been accelerating for about the last five billion years 1238 00:59:23,230 --> 00:59:26,800 out of the 14 billion year history of the universe. 1239 00:59:26,800 --> 00:59:28,830 There was a period where it was decelerating 1240 00:59:28,830 --> 00:59:31,819 until five billion years ago. 1241 00:59:31,819 --> 00:59:33,860 An implication of this is that inflation actually 1242 00:59:33,860 --> 00:59:34,860 is happening today. 1243 00:59:34,860 --> 00:59:36,840 This acceleration of the universe that we see 1244 00:59:36,840 --> 00:59:39,880 is very much like inflation, and we really interpret it 1245 00:59:39,880 --> 00:59:42,360 according to similar kind of physics. 1246 00:59:42,360 --> 00:59:44,670 We think it has to be caused by some kind 1247 00:59:44,670 --> 00:59:46,760 of a negative pressure, just as inflation 1248 00:59:46,760 --> 00:59:48,770 was caused by a negative pressure. 1249 00:59:51,650 --> 00:59:55,970 And this material that apparently fills space and has 1250 00:59:55,970 --> 00:59:58,737 negative pressure is what we call dark energy. 1251 00:59:58,737 --> 01:00:00,570 And dark energy is really just by definition 1252 01:00:00,570 --> 01:00:02,770 the stuff, whatever it is, that's 1253 01:00:02,770 --> 01:00:05,980 causing this acceleration. 1254 01:00:05,980 --> 01:00:08,650 If we ask, what is the dark energy, really? 1255 01:00:08,650 --> 01:00:11,170 I think everybody agrees there's a definite answer to that, 1256 01:00:11,170 --> 01:00:14,740 which is something like, who knows? 1257 01:00:14,740 --> 01:00:17,430 But there's also a most plausible candidate, 1258 01:00:17,430 --> 01:00:19,390 even though we don't know. 1259 01:00:19,390 --> 01:00:21,730 The most plausible candidate-- and other candidates 1260 01:00:21,730 --> 01:00:23,915 are not that different, really, but we'll 1261 01:00:23,915 --> 01:00:26,290 talk about the most plausible candidate-- which is simply 1262 01:00:26,290 --> 01:00:28,850 that dark energy is vacuum energy. 1263 01:00:28,850 --> 01:00:31,130 The energy of nothingness. 1264 01:00:31,130 --> 01:00:34,970 Now it may be surprising that nothingness can have energy. 1265 01:00:34,970 --> 01:00:37,700 But I'll talk about that, and it's really not so surprising. 1266 01:00:37,700 --> 01:00:39,840 I'll come back to that question. 1267 01:00:39,840 --> 01:00:43,197 But if dark energy is really just the energy of the vacuum, 1268 01:00:43,197 --> 01:00:45,030 that's completely consistent with everything 1269 01:00:45,030 --> 01:00:47,960 we know about, what we can measure, the expansion pattern 1270 01:00:47,960 --> 01:00:49,011 of the universe. 1271 01:00:49,011 --> 01:00:49,510 Yes. 1272 01:00:49,510 --> 01:00:52,378 AUDIENCE: Why is it that only in the last five billion years 1273 01:00:52,378 --> 01:00:54,585 has the universe started accelerating? 1274 01:00:54,585 --> 01:00:55,960 PROFESSOR: To start accelerating. 1275 01:00:55,960 --> 01:00:56,380 Right. 1276 01:00:56,380 --> 01:00:56,910 Right. 1277 01:00:56,910 --> 01:00:57,360 OK. 1278 01:00:57,360 --> 01:00:58,490 I'm now in a position to say that. 1279 01:00:58,490 --> 01:01:00,500 I wasn't quite when I made the first statement, 1280 01:01:00,500 --> 01:01:03,190 but now that I've said there's probably vacuum energy, 1281 01:01:03,190 --> 01:01:05,350 I can give you an answer. 1282 01:01:05,350 --> 01:01:07,880 Which is that vacuum energy, because it is just 1283 01:01:07,880 --> 01:01:10,859 the energy of the vacuum, does not change with time. 1284 01:01:10,859 --> 01:01:13,150 And that's the same as what I told you about the energy 1285 01:01:13,150 --> 01:01:14,360 density during inflation. 1286 01:01:14,360 --> 01:01:16,030 It's just a constant. 1287 01:01:16,030 --> 01:01:17,970 At the same time, ordinary matter 1288 01:01:17,970 --> 01:01:21,140 thins out as the universe expands, throwing off 1289 01:01:21,140 --> 01:01:24,130 in density like one over the cube of the volume. 1290 01:01:24,130 --> 01:01:26,580 So what happened was that the universe 1291 01:01:26,580 --> 01:01:29,630 was dominated by ordinary matter until about five 1292 01:01:29,630 --> 01:01:32,680 billion years ago, which produced attractive gravity 1293 01:01:32,680 --> 01:01:35,230 and caused the universe to slow. 1294 01:01:35,230 --> 01:01:37,680 But then about five billion years ago 1295 01:01:37,680 --> 01:01:41,460 the universe thinned out enough so that the ordinary matter 1296 01:01:41,460 --> 01:01:45,980 no longer dominated over the vacuum energy, and then 1297 01:01:45,980 --> 01:01:49,090 the vacuum energy started causing repulsion. 1298 01:01:49,090 --> 01:01:51,290 Vacuum energy was there all along causing repulsion, 1299 01:01:51,290 --> 01:01:53,830 but it was overwhelmed by the attractive gravity 1300 01:01:53,830 --> 01:01:57,660 of the ordinary matter until about five billion years ago. 1301 01:01:57,660 --> 01:01:58,807 Does that make sense? 1302 01:01:58,807 --> 01:01:59,390 AUDIENCE: Yes. 1303 01:01:59,390 --> 01:02:00,372 PROFESSOR: OK. 1304 01:02:00,372 --> 01:02:01,052 Good. 1305 01:02:01,052 --> 01:02:01,885 Any other questions? 1306 01:02:04,610 --> 01:02:06,070 OK. 1307 01:02:06,070 --> 01:02:06,652 So. 1308 01:02:06,652 --> 01:02:08,360 The first thing I want to talk about here 1309 01:02:08,360 --> 01:02:11,430 is why can nothing weigh something? 1310 01:02:11,430 --> 01:02:13,470 Why can nothing have energy? 1311 01:02:13,470 --> 01:02:14,970 And the answer is that actually this 1312 01:02:14,970 --> 01:02:17,920 is something the physicists are pretty clear on these days. 1313 01:02:17,920 --> 01:02:21,250 The quantum vacuum, unlike the classical vacuum, 1314 01:02:21,250 --> 01:02:23,480 is a very complicated state. 1315 01:02:23,480 --> 01:02:26,170 It's not really empty at all. 1316 01:02:26,170 --> 01:02:31,572 It really is a complicated jumble of vacuum fluctuations. 1317 01:02:31,572 --> 01:02:34,030 We think there's even a field called the Higgs field, which 1318 01:02:34,030 --> 01:02:35,488 you've probably heard of, which has 1319 01:02:35,488 --> 01:02:38,970 a nonzero value in the vacuum on average. 1320 01:02:38,970 --> 01:02:41,835 Things like the photon field, the electromagnetic field, 1321 01:02:41,835 --> 01:02:44,230 is constantly oscillating in the vacuum because 1322 01:02:44,230 --> 01:02:46,170 of the uncertainty principle, basically, 1323 01:02:46,170 --> 01:02:49,771 resulting in energy density in those fluctuations. 1324 01:02:49,771 --> 01:02:51,520 So there's no reason for the vacuum energy 1325 01:02:51,520 --> 01:02:54,160 to be zero, as far as we can tell. 1326 01:02:54,160 --> 01:02:56,990 But that doesn't mean that we understand its value. 1327 01:02:56,990 --> 01:02:59,820 The real problem from the point of view of fundamental physics 1328 01:02:59,820 --> 01:03:02,540 today is not understanding why the vacuum might 1329 01:03:02,540 --> 01:03:04,200 have a nonzero energy density. 1330 01:03:04,200 --> 01:03:09,230 The problem is understanding basically why it's so small. 1331 01:03:09,230 --> 01:03:11,440 And why is smallness a problem? 1332 01:03:11,440 --> 01:03:13,730 If you look at quantum field theory-- which we're not 1333 01:03:13,730 --> 01:03:16,060 going to learn in any detail-- but quantum field theory 1334 01:03:16,060 --> 01:03:18,720 says that, for example, the electromagnetic field 1335 01:03:18,720 --> 01:03:21,090 is constantly fluctuating. 1336 01:03:21,090 --> 01:03:24,290 Guaranteed so by the uncertainty principle. 1337 01:03:24,290 --> 01:03:27,510 And these fluctuations can have all wavelengths. 1338 01:03:27,510 --> 01:03:30,810 And every wavelength contributes to the energy density 1339 01:03:30,810 --> 01:03:32,990 of the vacuum fluctuations. 1340 01:03:32,990 --> 01:03:34,930 And there is no shortest wavelength. 1341 01:03:34,930 --> 01:03:36,950 There's a longest wavelength in any size box, 1342 01:03:36,950 --> 01:03:39,370 but there's no shortest wavelength. 1343 01:03:39,370 --> 01:03:41,370 So in fact, when you try to calculate the energy 1344 01:03:41,370 --> 01:03:43,700 density of the vacuum in the quantum field theory, 1345 01:03:43,700 --> 01:03:46,692 it diverges on the short wavelength side. 1346 01:03:46,692 --> 01:03:49,275 It becomes literally infinite as far as the formal calculation 1347 01:03:49,275 --> 01:03:51,895 is concerned because all wavelengths contribute, 1348 01:03:51,895 --> 01:03:55,320 and there is no shortest wavelength. 1349 01:03:55,320 --> 01:04:01,640 So what does this mean about the real physics? 1350 01:04:01,640 --> 01:04:05,450 We think it's not necessarily a problem with our understanding 1351 01:04:05,450 --> 01:04:06,570 of quantum field theory. 1352 01:04:06,570 --> 01:04:08,940 It really is, we think, just a limitation 1353 01:04:08,940 --> 01:04:13,280 of the range of validity of those assumptions. 1354 01:04:13,280 --> 01:04:16,076 They certainly-- quantum theory works extraordinarily well 1355 01:04:16,076 --> 01:04:20,780 when it's tested in laboratory circumstances. 1356 01:04:20,780 --> 01:04:23,580 So we think that at very short wavelengths, 1357 01:04:23,580 --> 01:04:26,490 something must happen to cut off this infinity. 1358 01:04:26,490 --> 01:04:29,060 And a good candidate for what happens at short wavelengths 1359 01:04:29,060 --> 01:04:31,340 to cut off the infinity is the effects 1360 01:04:31,340 --> 01:04:35,050 of quantum gravity, which we don't understand. 1361 01:04:35,050 --> 01:04:39,750 So one way of estimating the true energy density 1362 01:04:39,750 --> 01:04:41,880 as predicted by quantum field theory 1363 01:04:41,880 --> 01:04:45,490 is to cut things off at the Planck scale, the energy scale, 1364 01:04:45,490 --> 01:04:47,970 length scale, associated with quantum gravity-- which 1365 01:04:47,970 --> 01:04:50,611 is about 10 to the minus 33 centimeters. 1366 01:04:50,611 --> 01:04:52,610 And if you do that, you can calculate the number 1367 01:04:52,610 --> 01:04:55,110 for the energy density of the electromagnetic field 1368 01:04:55,110 --> 01:04:58,280 of the vacuum and get a finite number. 1369 01:04:58,280 --> 01:05:00,940 But it's too large. 1370 01:05:00,940 --> 01:05:04,040 And too large not by a little bit, but by a lot. 1371 01:05:04,040 --> 01:05:07,800 It's too large by 120 orders of magnitude. 1372 01:05:07,800 --> 01:05:12,450 So we are way off in terms of understanding why the vacuum 1373 01:05:12,450 --> 01:05:18,430 energy is what it is since our naive estimates say it should 1374 01:05:18,430 --> 01:05:21,570 be maybe 120 orders of magnitude larger. 1375 01:05:21,570 --> 01:05:26,870 Now I should add that there is still a way out here. 1376 01:05:26,870 --> 01:05:28,520 The energy that we calculate here 1377 01:05:28,520 --> 01:05:31,530 is one contribution to the total vacuum energy. 1378 01:05:31,530 --> 01:05:33,730 There are negative contributions as well. 1379 01:05:33,730 --> 01:05:36,270 If you calculate the fluctuations of the electron 1380 01:05:36,270 --> 01:05:38,880 field, that turns out to be negative in its contribution 1381 01:05:38,880 --> 01:05:40,350 to the energy. 1382 01:05:40,350 --> 01:05:43,050 And it's always possible that these numbers cancel-- 1383 01:05:43,050 --> 01:05:47,810 or cancel almost exactly-- but we don't know why they should. 1384 01:05:47,810 --> 01:05:50,810 So basically there's a big question mark theoretically 1385 01:05:50,810 --> 01:05:54,770 on what we would predict for the energy density of the vacuum. 1386 01:05:57,350 --> 01:05:57,850 Let's see. 1387 01:05:57,850 --> 01:05:59,090 What should I do here? 1388 01:05:59,090 --> 01:06:03,147 I am not going to be able to finish this lecture. 1389 01:06:03,147 --> 01:06:04,730 I think it's worth finishing, however. 1390 01:06:04,730 --> 01:06:07,850 So I think what I'll do is I'll maybe go through this slide 1391 01:06:07,850 --> 01:06:11,680 and then we'll just stop, and we'll pick up again next time. 1392 01:06:11,680 --> 01:06:14,010 There are just a few more slides to show. 1393 01:06:14,010 --> 01:06:17,230 But I think it's an interesting story worth finishing. 1394 01:06:17,230 --> 01:06:19,160 But to come to a good stopping place here-- 1395 01:06:19,160 --> 01:06:21,760 we still have a minute and a half, I think. 1396 01:06:21,760 --> 01:06:24,790 I want to say a little bit about the landscape of string theory, 1397 01:06:24,790 --> 01:06:28,510 which is going to be a possible explanation-- only possible, 1398 01:06:28,510 --> 01:06:32,440 it's very speculative here-- but one possible explanation which 1399 01:06:32,440 --> 01:06:36,780 combines inflation, the eternal inflation, and string theory 1400 01:06:36,780 --> 01:06:40,050 produces a possible explanation for this very small vacuum 1401 01:06:40,050 --> 01:06:42,460 energy that we observe. 1402 01:06:42,460 --> 01:06:45,050 It's based on the idea that string theory does not 1403 01:06:45,050 --> 01:06:47,330 have the unique vacuum. 1404 01:06:47,330 --> 01:06:51,030 For many years string theorists sought 1405 01:06:51,030 --> 01:06:54,984 to find the vacuum of string theory with no success. 1406 01:06:54,984 --> 01:06:56,400 They just couldn't figure out what 1407 01:06:56,400 --> 01:06:58,670 the vacuum of string theory would look like. 1408 01:06:58,670 --> 01:07:02,440 And then a little more than 10 years ago many string theorists 1409 01:07:02,440 --> 01:07:04,550 began to converge around the idea 1410 01:07:04,550 --> 01:07:07,150 that maybe they could not find a vacuum because there 1411 01:07:07,150 --> 01:07:10,000 is no unique vacuum to string theory. 1412 01:07:10,000 --> 01:07:16,520 Instead, what they now claim is that there's 1413 01:07:16,520 --> 01:07:19,660 a colossal number-- they bandy around numbers like 10 1414 01:07:19,660 --> 01:07:25,050 to the 500th power-- a colossal number of metastable states, 1415 01:07:25,050 --> 01:07:28,410 which are long lived, any one of which 1416 01:07:28,410 --> 01:07:32,000 could look like a vacuum for a long period of time, 1417 01:07:32,000 --> 01:07:35,110 even though ultimately it might decay or tunnel into one 1418 01:07:35,110 --> 01:07:38,710 of the other metastable states. 1419 01:07:38,710 --> 01:07:41,790 So this is called the landscape of string theory. 1420 01:07:41,790 --> 01:07:45,250 This huge set of vacuum like states, 1421 01:07:45,250 --> 01:07:49,202 any one of which could be the vacuum that fills a given 1422 01:07:49,202 --> 01:07:50,410 pocket universe, for example. 1423 01:07:53,700 --> 01:07:57,920 When one combines this with the idea of eternal inflation, 1424 01:07:57,920 --> 01:08:01,320 then one reaches the conclusion that eternal inflation 1425 01:08:01,320 --> 01:08:04,240 would very likely populate all of these 10 1426 01:08:04,240 --> 01:08:06,590 to the 500 or more vacua. 1427 01:08:06,590 --> 01:08:08,680 That is, different pocket universes 1428 01:08:08,680 --> 01:08:11,340 would have different kinds of vacuum inside them, which 1429 01:08:11,340 --> 01:08:15,270 would be determined randomly as the pocket universes nucleate, 1430 01:08:15,270 --> 01:08:19,200 as they break off from this inflating backbone. 1431 01:08:21,790 --> 01:08:23,479 And then we would have a multiverse 1432 01:08:23,479 --> 01:08:26,287 which would consist of many, many-- 10 1433 01:08:26,287 --> 01:08:29,069 to the 500 or more-- different kinds of vacua 1434 01:08:29,069 --> 01:08:30,535 in different pocket universes. 1435 01:08:33,609 --> 01:08:36,500 Under this assumption, ultimately string theory 1436 01:08:36,500 --> 01:08:38,689 would be the assumed laws of physics 1437 01:08:38,689 --> 01:08:41,500 that would govern everything. 1438 01:08:41,500 --> 01:08:43,979 But if you were living in one of these pocket universes, 1439 01:08:43,979 --> 01:08:48,170 you actually see apparent laws of physics that would look very 1440 01:08:48,170 --> 01:08:51,029 different from other pocket universe's. 1441 01:08:51,029 --> 01:08:53,229 The point is that the physics that we actually 1442 01:08:53,229 --> 01:08:56,979 see and measure is low energy physics compared to the energy 1443 01:08:56,979 --> 01:09:00,130 scales of the string theory. 1444 01:09:00,130 --> 01:09:04,930 So what we are seeing are just small fluctuations 1445 01:09:04,930 --> 01:09:07,330 in the ultimate scheme of things about the vacuum 1446 01:09:07,330 --> 01:09:09,670 that we live in. 1447 01:09:09,670 --> 01:09:12,660 So the very particle spectrum that we see, 1448 01:09:12,660 --> 01:09:16,310 the fact that we see electrons and quarks, quarks 1449 01:09:16,310 --> 01:09:19,310 that combine to form protons and neutrons-- 1450 01:09:19,310 --> 01:09:22,037 could be peculiar to our particular pocket. 1451 01:09:22,037 --> 01:09:24,620 And in other pockets there could be completely different kinds 1452 01:09:24,620 --> 01:09:27,100 of particles, which are just oscillations 1453 01:09:27,100 --> 01:09:29,979 about different kinds of vacuum. 1454 01:09:29,979 --> 01:09:31,819 So even though the laws of physics 1455 01:09:31,819 --> 01:09:34,340 would in principle be the same everywhere-- 1456 01:09:34,340 --> 01:09:36,765 the laws of string theory-- in practice the 1457 01:09:36,765 --> 01:09:38,140 observed laws of physics would be 1458 01:09:38,140 --> 01:09:40,555 very different from one pocket to another. 1459 01:09:40,555 --> 01:09:41,930 And in particular since there are 1460 01:09:41,930 --> 01:09:44,319 different vacua in the different pockets, 1461 01:09:44,319 --> 01:09:46,520 the vacuum energy density would be 1462 01:09:46,520 --> 01:09:48,510 different in different pockets. 1463 01:09:48,510 --> 01:09:53,420 And that variability of the vacuum energy density 1464 01:09:53,420 --> 01:09:57,220 provides a possible answer to why we see such a small vacuum 1465 01:09:57,220 --> 01:09:57,970 energy. 1466 01:09:57,970 --> 01:10:01,610 And we'll talk more about that next time on Tuesday. 1467 01:10:01,610 --> 01:10:03,280 See you then.