1 00:00:00,012 --> 00:00:07,067 We now come to address Inflation. Which is the factor, the standard theory of 2 00:00:07,067 --> 00:00:12,875 Quantum Cosmology today. It really started in 1980, where Alan 3 00:00:12,875 --> 00:00:20,084 Guth physicist at MIT came up with what he called a spectacular realization. 4 00:00:20,084 --> 00:00:26,198 This is a page from his journaled time. some of these ideas have been already 5 00:00:26,198 --> 00:00:29,118 discussed by others but not known to Guth. 6 00:00:29,118 --> 00:00:35,202 And since then many other people have improved the theory and added more to it. 7 00:00:35,202 --> 00:00:41,120 Well, the reason why everybody got so excited and why inflation has achieved 8 00:00:41,120 --> 00:00:47,212 such a great acceptance is that it solves three key cosmological problems which had 9 00:00:47,212 --> 00:00:52,123 no obvious solution before. The first one of those is so called 10 00:00:52,123 --> 00:00:57,532 flatness problem, why is the universe so close to being exactly flat. 11 00:00:57,532 --> 00:01:02,947 The second is the horizon problem, why was cosmic microwaves so uniform? We'll 12 00:01:02,947 --> 00:01:07,747 explain both of these in a moment. The third one is less obvious and this 13 00:01:07,747 --> 00:01:13,642 is, where there are no magnetic monopoles observable today? Whereas many Big Bang 14 00:01:13,642 --> 00:01:18,902 theories predicted there should be copious amounts of them created in the 15 00:01:18,902 --> 00:01:23,177 early universe. Inflation also accounts for the observed 16 00:01:23,177 --> 00:01:29,179 power spectrum of galaxy clustering and those are extensively fluctuations left 17 00:01:29,179 --> 00:01:32,392 over from an earlier phase of the universe. 18 00:01:32,392 --> 00:01:38,909 It also predicts the existence of random cosmic gravitational wave background, but 19 00:01:38,909 --> 00:01:42,882 we're very far from being able to detect such a thing. 20 00:01:42,882 --> 00:01:48,388 And implies that our universe is just a small part of a much, much, much bigger 21 00:01:48,388 --> 00:01:52,089 universe. Let's tackle the flatness problem first. 22 00:01:52,089 --> 00:01:56,813 In Friedmann Lemaitre models, omega always evolves away from unity. 23 00:01:56,813 --> 00:02:02,323 So if the universe was slightly negative curvature, it'll become more so as it 24 00:02:02,323 --> 00:02:05,683 evolves. If it was slightly positive curvature 25 00:02:05,683 --> 00:02:12,076 it'll become more so as it evolves. A great demonstration of that is shown in 26 00:02:12,076 --> 00:02:18,511 this diagram [UNKNOWN] my right. It shows the density of the universe, one 27 00:02:18,511 --> 00:02:25,552 nanosecond after the big bang and it was 400 something sextillion 16 grams per 28 00:02:25,552 --> 00:02:30,043 cubic centimeter. Add one more gram per cubic centimeter, 29 00:02:30,043 --> 00:02:33,067 universe becomes closed and will collapse. 30 00:02:33,067 --> 00:02:36,859 Subtract one, and universe goes to expansion forever. 31 00:02:36,859 --> 00:02:42,368 So this is extremely sensitive, even the slightest deviation of omega equal one 32 00:02:42,368 --> 00:02:47,159 from the early universe would map into a much bigger deviation today. 33 00:02:47,159 --> 00:02:52,204 And yet we know the universe is very close to flat, so we must have started 34 00:02:52,204 --> 00:02:56,565 really really close to flat, if not absolutely flat. 35 00:02:56,565 --> 00:03:00,565 The horizon problem can be stated this way at any given time. 36 00:03:00,565 --> 00:03:05,824 you can receive signals from points that are within the time elapse from the big 37 00:03:05,824 --> 00:03:08,737 bang. And the particle-horizon distance is 38 00:03:08,737 --> 00:03:13,542 three times speed of the light times, the age of the universe at the time. 39 00:03:13,542 --> 00:03:19,112 Now remember that early on scale factor goes as time to the 2/3 power, and so it 40 00:03:19,112 --> 00:03:24,527 means that the horizon expands faster than the universe, and as time goes on 41 00:03:24,527 --> 00:03:28,027 you get to see more and more objects come into it. 42 00:03:28,027 --> 00:03:33,367 Now look at cosmic micro background. It originates from roughly [UNKNOWN] 43 00:03:33,367 --> 00:03:39,627 1000, and so it's temperature back then was about 10^4.5 higher than it is today. 44 00:03:39,627 --> 00:03:44,822 At that time the horizon distance was given by the formula that I just 45 00:03:44,822 --> 00:03:49,847 mentioned above, and since then it's expanded by a factor of 1000. 46 00:03:49,847 --> 00:03:53,832 However, our horizon distance is bigger than that. 47 00:03:53,832 --> 00:03:59,147 And therefore, there should be many disconnected, causally disconnected 48 00:03:59,147 --> 00:04:04,452 regions in the sky, which were not in a causal contact at the time with when 49 00:04:04,452 --> 00:04:09,867 microwave background was released. So, even though we can see that there is 50 00:04:09,867 --> 00:04:15,636 one sky now, back then, patches of micro background scalar that are more than say 51 00:04:15,636 --> 00:04:18,772 two degrees apart were not in a causal contact. 52 00:04:18,772 --> 00:04:23,671 And yet, cosmic micro background is uniform to few parts in a million. 53 00:04:23,671 --> 00:04:29,066 So how did these independent pieces of universe know to have same temperature 54 00:04:29,066 --> 00:04:34,372 within a part in a million universes with which they could not have had physical 55 00:04:34,372 --> 00:04:37,539 contact. The monopole problem is somewhat generic 56 00:04:37,539 --> 00:04:42,537 to the particle physics, and prediction is that copious numbers of those will be 57 00:04:42,537 --> 00:04:48,134 generated during the grand unified theory transition, the face transition. 58 00:04:48,134 --> 00:04:51,863 Yet none have been found despite many intensive searches. 59 00:04:51,863 --> 00:04:56,665 Not only that, but their masses are supposed to be so high that coupled with 60 00:04:56,665 --> 00:05:01,012 density, they would totally dominate the dynamics of the universe. 61 00:05:01,012 --> 00:05:06,069 A generic expectation is that future theory of everything that unifies gravity 62 00:05:06,069 --> 00:05:11,460 with other interactions, all interactions are unified into one around planck time 63 00:05:11,460 --> 00:05:15,608 or there abouts. The universe undergoes a phase 64 00:05:15,608 --> 00:05:19,605 transition. Then the universe undergoes a phase where 65 00:05:19,605 --> 00:05:25,392 gravity splits from the outer forces, and things remain roughly the same on the 66 00:05:25,392 --> 00:05:31,179 logorythmic time axis by almost 10 more powers of 10 when there is another phase 67 00:05:31,179 --> 00:05:34,982 transition. What is postulated here, is that physical 68 00:05:34,982 --> 00:05:38,538 vacuum was not in its actual ground state at the time. 69 00:05:38,538 --> 00:05:43,650 But it was at higher state, just like in atoms there is a ground state and then 70 00:05:43,650 --> 00:05:47,650 electrons can go to higher orbits, and have excited states. 71 00:05:47,650 --> 00:05:51,982 Also supposedly the universe, the vac, physical vacuum itself, 72 00:05:51,982 --> 00:05:57,192 could've been in such a higher state. Somehow, in mechanisms for this are very 73 00:05:57,192 --> 00:06:00,081 complex and beyond the scope of this class. 74 00:06:00,081 --> 00:06:05,241 The vacuum undergoes a phase transition going to the actual ground state, the 75 00:06:05,241 --> 00:06:10,130 true vac and in that process, vast amounts of energy are released and that 76 00:06:10,130 --> 00:06:13,492 energy is used to drive exponential expansion. 77 00:06:13,492 --> 00:06:19,809 Here is one schematic way to show it. The potential energy of some scale or 78 00:06:19,809 --> 00:06:24,230 field Pi is plotted against potentially itself. 79 00:06:24,230 --> 00:06:30,441 And if universe is a center of a high plateau zero this is a metastable state. 80 00:06:30,441 --> 00:06:35,269 It will eventually roll down into the true vacuum, which is at some finite 81 00:06:35,269 --> 00:06:38,733 value of Pi, and may even slosh around a little bit. 82 00:06:38,733 --> 00:06:43,609 So in this schematic, the universe rolls down the scalar field potential. 83 00:06:43,609 --> 00:06:48,925 So the decay of the field reheats the universe from that excess energy and all 84 00:06:48,925 --> 00:06:53,972 of the matter/energy content of the universe can be created in that process. 85 00:06:53,972 --> 00:06:59,145 So the universe undergoes phase transition and releases this latent heat 86 00:06:59,145 --> 00:07:03,711 inflating exponentially. This could be just one of the many many 87 00:07:03,711 --> 00:07:09,354 bubbles in a much larger universe that expand and maybe collide which is process 88 00:07:09,354 --> 00:07:13,658 called reheating. However, this is something that has never 89 00:07:13,658 --> 00:07:17,367 been observed yet. Now the energy density of a physical 90 00:07:17,367 --> 00:07:20,672 vacuum can be described as a cosmological constant. 91 00:07:20,672 --> 00:07:25,667 This is not the cosmological constant of today, but some much larger value from 92 00:07:25,667 --> 00:07:29,442 the earlier universe. In that case the Friedmann equation is 93 00:07:29,442 --> 00:07:34,107 give fairly simply and has an obvious solution, an exponential expansion. 94 00:07:34,107 --> 00:07:37,182 It turns out that these inflationary models. 95 00:07:37,182 --> 00:07:44,595 This exponential expansion phase goes for about 100 e folding times or 40 orders of 96 00:07:44,595 --> 00:07:49,766 magnitude in size. And since the deviation of the density 97 00:07:49,766 --> 00:07:54,454 parameter from unity also goes from exponentially. 98 00:07:54,454 --> 00:08:00,871 That means, there was incredibly finely tuned to be close to unity to begin with. 99 00:08:00,871 --> 00:08:06,673 So here is a schematic expansion diagram, it's plotted as 1 plus redshift rather 100 00:08:06,673 --> 00:08:10,886 than 1 over the quantity, which would be the scale factor. 101 00:08:10,886 --> 00:08:15,698 So there is a rapid initial expansion, and then universe enters into a 102 00:08:15,698 --> 00:08:20,400 traditional Friedmann Lemaitre phase. So how does this solve the flatness 103 00:08:20,400 --> 00:08:23,277 problem? Well think about, this as follows. 104 00:08:23,277 --> 00:08:27,820 You can start with the region on a sphere, or this is now a 2 dimensional 105 00:08:27,820 --> 00:08:33,422 equivalent of 4 dimensional space time. If you inflate this sphere by a large 106 00:08:33,422 --> 00:08:39,988 amount, that region will appear spatially flat, and by that same token this great 107 00:08:39,988 --> 00:08:46,315 expansion of the universe essentially flattens the local curvature which might 108 00:08:46,315 --> 00:08:51,574 have been more substantial. So the density parameter differs from 109 00:08:51,574 --> 00:08:56,352 unity by an epsilon, a very tiny number At the same time to solves the horizon 110 00:08:56,352 --> 00:08:59,542 problem. Space can expand faster than the speed of 111 00:08:59,542 --> 00:09:03,952 light, so the regions that were constantly disjoint at the time of the 112 00:09:03,952 --> 00:09:08,967 recombination might have been spatially close to each other at the beginning of 113 00:09:08,967 --> 00:09:12,756 the inflation. They might be really adjacent to each 114 00:09:12,756 --> 00:09:18,607 other and that, that's why they have same energy density or same temperature of the 115 00:09:18,607 --> 00:09:23,372 micro background today. The inflation carries them apart, and so 116 00:09:23,372 --> 00:09:28,954 by the time, by the end of the inflation they were no longer in a casual contact. 117 00:09:28,954 --> 00:09:33,335 But nevertheless, prior to that, they were nicely termalized. 118 00:09:33,335 --> 00:09:38,203 Inflation also tackled the origin of the large scale structure we see. 119 00:09:38,203 --> 00:09:43,173 In quantum physics, the vacuum is not empty but it's populated by virtual 120 00:09:43,173 --> 00:09:47,275 particle-antiparticle pairs that appear and dissappears. 121 00:09:47,275 --> 00:09:52,582 subject to the uncertainty principle. They cause essentially quantum 122 00:09:52,582 --> 00:09:56,303 fluctuations of energy density in the early universe. 123 00:09:56,303 --> 00:10:01,518 Now inflation blows up these minute quantum fluctuations of physical vacuum 124 00:10:01,518 --> 00:10:05,415 to enormous size. Where in fact, where they can be really 125 00:10:05,415 --> 00:10:09,622 seeds of the large skill structure that we observed today. 126 00:10:09,622 --> 00:10:14,677 Is an remarkable prediction, that time quantum fluctuations can result in larger 127 00:10:14,677 --> 00:10:19,162 structures that they're observed. And there is a specific prediction of the 128 00:10:19,162 --> 00:10:23,777 functional form of the power spectrum of these fluctuations, which turns out 129 00:10:23,777 --> 00:10:26,617 corresponse fairly closely to what's observed. 130 00:10:26,617 --> 00:10:31,563 Note that this is not approve of inflation because one can come up with 131 00:10:31,563 --> 00:10:35,980 different ways to reach the same observed state if large scale structure. 132 00:10:35,980 --> 00:10:39,464 But the consistency is cert, certainly very encouraging. 133 00:10:39,464 --> 00:10:42,449 Next time, we'll talk about even earlier universe.