1 00:00:00,012 --> 00:00:06,017 So, I like to describe some of the solutions people have come up with for 2 00:00:06,017 --> 00:00:10,472 the 3 middle problems that we discussed. The horizon problem, 3 00:00:10,472 --> 00:00:14,307 the flatness problem, and the relic problem. 4 00:00:14,307 --> 00:00:20,737 And the collection of ideas that are developed to addressed this go under the 5 00:00:20,737 --> 00:00:26,376 name of inflation. This was first publicly, in a well known 6 00:00:26,376 --> 00:00:33,056 way developed by Allen Guth in 1980. Although there were Soviet efforts that 7 00:00:33,056 --> 00:00:39,082 we did not hear about until later, and Guth's idea is the following. Imagine 8 00:00:39,082 --> 00:00:46,187 that at early times, at 10 to the minus 36 seconds below the gut energy scale, so 9 00:00:46,187 --> 00:00:53,371 after the grand unified theory time but before the electro weak transition, the 10 00:00:53,371 --> 00:01:00,861 universe underwent exponential expansion by many orders of magnitude, 10 to the 30 11 00:01:00,861 --> 00:01:04,000 say. Some large number, 10^50, so an 12 00:01:04,000 --> 00:01:09,762 exponential expansion during which the scale factor grew by a factor of 10^50. 13 00:01:09,762 --> 00:01:16,223 what does that mean? That means, remember an exponential expansion, once event 14 00:01:16,223 --> 00:01:22,270 horizon continually shrinks, and so our particle horizon, what we can see After, 15 00:01:22,270 --> 00:01:28,302 that expansion is the small fraction of it was then one particle horizon. 16 00:01:28,302 --> 00:01:34,749 The entire observable universe was some tiny little fraction, of one region, that 17 00:01:34,749 --> 00:01:39,012 was the pre-inflation of the pre-inflation horizon. 18 00:01:39,012 --> 00:01:44,145 so that solves the horizon problem. You give things 10^-36 seconds to 19 00:01:44,145 --> 00:01:47,387 equilibrate within the region of one horizon. 20 00:01:47,387 --> 00:01:52,723 And then, you blow them up, so they, get pushed out, outside of the horizon. 21 00:01:52,723 --> 00:01:58,321 And then, all the things that we are slowly seeing, moving into our particle 22 00:01:58,321 --> 00:02:04,051 horizon, because our particle horizon growth are actually see things that we 23 00:02:04,051 --> 00:02:08,965 have seen before, back in the first 10^-36 seconds, and so there is no news. 24 00:02:08,965 --> 00:02:13,657 There's no surprise that the cosmic microwave background is so uniform. 25 00:02:13,657 --> 00:02:19,460 It's so uniform precisely because we have inflated and all the things that are out 26 00:02:19,460 --> 00:02:24,515 there are things that were causally connected with us prior to inflation. 27 00:02:24,515 --> 00:02:29,382 Similarly, the exponential inflation drives omega to 1. You can see that from 28 00:02:29,382 --> 00:02:33,412 the same equation that gave us the problem of fine tuning before. whatever 29 00:02:33,412 --> 00:02:38,372 omega, remember that H squared omega minus 1 is always equal to this. in this 30 00:02:38,372 --> 00:02:43,142 case an exponential expansion, the Hubble Constant is a constant, remember, and so 31 00:02:43,142 --> 00:02:47,287 what that means is that as a grows by a factor of 10 to the 50 say, this 32 00:02:47,287 --> 00:02:51,887 denominator gets bigger by a factor of 10 to the 100 and omega minus 1 has to 33 00:02:51,887 --> 00:02:56,537 shrink by a factor of 10 to the 100. So whatever omega you started with, by 34 00:02:56,537 --> 00:03:01,322 the end of inflation you have omega equals 1 and then you start the radiation 35 00:03:01,322 --> 00:03:06,222 dominated area of our universe with omega equals 1 to a very high precision. 36 00:03:06,222 --> 00:03:11,132 And therefore it's not surprising that we end up with omega equals 1 today. 37 00:03:11,132 --> 00:03:16,737 And similarly, whatever density of relics you think that the gut transition has 38 00:03:16,737 --> 00:03:20,242 produced is now decreased by [SOUND] spreading them out. 39 00:03:20,242 --> 00:03:24,857 And if you have expansion by scale factor growing by 10 to the 50, 40 00:03:24,857 --> 00:03:28,192 the relic density is diluted by 10 to the 150, 41 00:03:28,192 --> 00:03:32,019 and you don't have a problem with the fact that we have not discovered 42 00:03:32,019 --> 00:03:36,434 monopoles. So inflation is a great idea, and the question is, what does that mean? 43 00:03:36,434 --> 00:03:39,942 So we understand the kinematics. We understand how to describe 44 00:03:39,942 --> 00:03:44,146 exponentially expanding universes. We'll use that to describe our future, 45 00:03:44,146 --> 00:03:48,591 but what does it mean, how do you have, ha-, what is the dynamics, what is the 46 00:03:48,591 --> 00:03:51,605 how do you turn a cosmological constant on and then off? 47 00:03:51,605 --> 00:03:55,983 Remember that we had sort of ideas in the context of quantum field theories for 48 00:03:55,983 --> 00:03:59,419 generating cosmological constants, and they were indeed huge. 49 00:03:59,419 --> 00:04:04,049 But how do you turn them on and off? Well in these quantum field theories and these 50 00:04:04,049 --> 00:04:08,642 guts there are such things as sort of tunable vacuum energy densities 51 00:04:08,642 --> 00:04:13,417 associated to expectation values of fields, sort of parameters, dynamical 52 00:04:13,417 --> 00:04:18,617 degrees of freedom of these theories. The detail, a little bit beyond what we 53 00:04:18,617 --> 00:04:23,917 need, you can find, and Gus's idea that the universe gets trapped in some false 54 00:04:23,917 --> 00:04:26,812 vacuum. This has large energy density. 55 00:04:26,812 --> 00:04:32,112 That triggers inflation and this lasts for a short time before the universe sort 56 00:04:32,112 --> 00:04:36,827 of tunnels, decays out of this false vacuum to the true vacuum with lowered 57 00:04:36,827 --> 00:04:39,897 energy. That energy difference is then released 58 00:04:39,897 --> 00:04:44,047 that heats the universe. So the universe had been super-cooled in 59 00:04:44,047 --> 00:04:49,022 some sense and then gets re-heated. The exit from the inflationary period 60 00:04:49,022 --> 00:04:54,804 into, is, into the current era, into the true vacuum has all kinds of what's 61 00:04:54,804 --> 00:04:59,834 called graceful exit problems. So a model was proposed called new 62 00:04:59,834 --> 00:05:05,344 inflation, or slow roll inflation, in which this tunneling event from a 63 00:05:05,344 --> 00:05:12,169 supercooled bubble-nucleation type phase transition like boiling water is replaced 64 00:05:12,169 --> 00:05:17,109 by a very slow transition where the inflation era is a slow roll. 65 00:05:17,109 --> 00:05:22,497 Where this parameter is rather than tunneling suddenly is very slowly 66 00:05:22,497 --> 00:05:26,427 evolving, and then sinking into the true vacuum and 67 00:05:26,427 --> 00:05:31,477 then subject to damped oscillations, which is how it re-heats the universe. 68 00:05:31,477 --> 00:05:37,077 new inflation had it's own issues. an improved version or a modified version 69 00:05:37,077 --> 00:05:42,827 with other features and problems called chaotic inflation, was proposed where the 70 00:05:42,827 --> 00:05:48,648 phase transition is gone alltogether and quantum fluctuations play the role of 71 00:05:48,648 --> 00:05:53,887 moving the field away from the actual vacuum whence it slowly rolls, and this 72 00:05:53,887 --> 00:05:57,759 occurs locally. And the idea is that one of these quantum 73 00:05:57,759 --> 00:06:03,928 fluctuation, fluctuations, in some region of The universe creates larger energy 74 00:06:03,928 --> 00:06:07,387 density. This region then inflates very rapidly. 75 00:06:07,387 --> 00:06:13,127 the fluctuation is then very rapidly thrown outside the particle horizon, and 76 00:06:13,127 --> 00:06:17,690 therefore can no longer decay. It's sort of frozen in, and then a new 77 00:06:17,690 --> 00:06:22,603 fluctuation occurs and that too is, blows up and is ejected from the horizon. 78 00:06:22,603 --> 00:06:28,532 And so fluctuations are frozen in as they inflate, and this led to the idea that is 79 00:06:28,532 --> 00:06:31,613 the sort of topical one called eternal inflation. 80 00:06:31,613 --> 00:06:36,408 In eternal inflation, what one really imagines that you have a universe with a 81 00:06:36,408 --> 00:06:40,627 large vacuum energy, so it's exponentially expanding and always has 82 00:06:40,627 --> 00:06:44,223 been. And if it's infinite in that it expands 83 00:06:44,223 --> 00:06:48,125 exponentially. small regions, of the universe, can 84 00:06:48,125 --> 00:06:51,781 spontaneously decay to vacuum, of smaller vacuum energy. 85 00:06:51,781 --> 00:06:57,631 So these regions are still exponentially expanding, but exponentially slower, than 86 00:06:57,631 --> 00:07:00,939 the The the ambient, if you want universe, 87 00:07:00,939 --> 00:07:04,969 are these baby universe. They pop off and from the point of view 88 00:07:04,969 --> 00:07:10,005 of the large universe, since they're not expanding fast enough, their intersection 89 00:07:10,005 --> 00:07:15,066 with the universe, with the, the universe they came from is exponentially shrinking 90 00:07:15,066 --> 00:07:20,020 and on the other hand these regions are inflating, and so they undergo inflation 91 00:07:20,020 --> 00:07:25,102 and can then re-heat and then produce the entire history of our universe. 92 00:07:25,102 --> 00:07:29,747 And regions within them can further bubble off to even lower values of 93 00:07:29,747 --> 00:07:34,537 lambda, and so you get this sort of a fleas on fleas picture of inflation. 94 00:07:34,537 --> 00:07:38,942 And the result is many disconnected, causally disconnected patches. 95 00:07:38,942 --> 00:07:43,583 This is the so-called multiverse. I have a feeling that I'm beginning to 96 00:07:43,583 --> 00:07:47,197 talk about fantasies. Is any is this real, does any of this 97 00:07:47,197 --> 00:07:51,988 mean anything for us, and the idea indeed is that exponential inflation can freeze 98 00:07:51,988 --> 00:07:55,207 fluctuations. If we have some fluctuation and then 99 00:07:55,207 --> 00:07:59,322 during the inflationary period, the wavelength of this grows beyond the 100 00:07:59,322 --> 00:08:04,035 particular horizon, can no longer decay, just as it could not have formed at that 101 00:08:04,035 --> 00:08:06,628 size. And what that means is that these frozen 102 00:08:06,628 --> 00:08:11,293 fluctuations are the inhomogeneieties around which dark matter and then 103 00:08:11,293 --> 00:08:15,949 subsequently barionic matter can collect so these are the seeds for structure 104 00:08:15,949 --> 00:08:18,905 formation. We've not hand the time to discuss the 105 00:08:18,905 --> 00:08:22,835 theory of structure formation. It's also a little bit technical, 106 00:08:22,835 --> 00:08:27,648 but basically this makes predictions, these models make predictions about the 107 00:08:27,648 --> 00:08:32,362 kind of distribution of clusters and galaxies that you might expect. And so, 108 00:08:32,362 --> 00:08:37,047 in some sense, a model that predicts some kind of inflationary scenario, will also 109 00:08:37,047 --> 00:08:41,657 make a prediction about the structure and the spectrum of perturbations, which will 110 00:08:41,657 --> 00:08:45,352 lead to a prediction about inhomogeneities in our actual universe, 111 00:08:45,352 --> 00:08:47,772 which you might actually compare with data. 112 00:08:47,772 --> 00:08:53,752 So, in an indirect way, these causally disconnected multi-verse regions might 113 00:08:53,752 --> 00:08:59,440 actually be, is part of some larger model, something you could verify.