1 00:00:00,012 --> 00:00:05,152 We now turn our attention to structure formation in the universe. 2 00:00:05,152 --> 00:00:09,953 Actually since the original disappointment of the failure of 3 00:00:09,953 --> 00:00:15,596 classical cosmological tests due to galaxy evolution in 1970s until the 4 00:00:15,596 --> 00:00:19,232 revival of precision cosmology in late 1990s. 5 00:00:19,232 --> 00:00:22,801 This was the main subject of cosmological research. 6 00:00:22,801 --> 00:00:27,989 So here is the problem in the nutshell. We see the dance defluxuations in the 7 00:00:27,989 --> 00:00:32,951 early universe imprinted on the cosmic microbe background photosphere. 8 00:00:32,951 --> 00:00:38,560 They're roughly parts in a million. Today, we see a large-scale structure, 9 00:00:38,560 --> 00:00:43,590 clusters, filaments, voids with density contracts of about 100. 10 00:00:43,590 --> 00:00:49,616 And then, within them there are galaxies whose average density within say half 11 00:00:49,616 --> 00:00:55,621 life radius is about million times larger than the surrounding So how do go from 12 00:00:55,621 --> 00:01:00,935 fluctuation, that there a part in a million, to large scare structure, that 13 00:01:00,935 --> 00:01:06,561 is factor of 100 over dense to galaxy that are, factor million over dense and 14 00:01:06,561 --> 00:01:09,228 that is the job. So we believe that the original 15 00:01:09,228 --> 00:01:13,504 fluctuations came from quantum fluctuations in the early universe that 16 00:01:13,504 --> 00:01:17,946 you know due to fluctuations in the number of density of particles and then 17 00:01:17,946 --> 00:01:22,891 they're inflated through the inflationary era to the large scale structures or are 18 00:01:22,891 --> 00:01:28,032 the seeds of large scale structures. The matter then falls into them, and the 19 00:01:28,032 --> 00:01:32,607 density contrast grows. So the observed thing is, fluctuations in 20 00:01:32,607 --> 00:01:37,832 micro background, is radiation and variations that are coupled before the 21 00:01:37,832 --> 00:01:40,907 recombination, which are parts in a million. 22 00:01:40,907 --> 00:01:45,932 But we also observe, galaxy-like structures at the [UNKNOWN] greater than 23 00:01:45,932 --> 00:01:48,982 6. Those are luminous quasars and Even some 24 00:01:48,982 --> 00:01:53,607 real galaxies, and so we know that at least some little pockets of the universe 25 00:01:53,607 --> 00:01:58,102 have achieved the density contrast which are not the part in a million, but a 26 00:01:58,102 --> 00:02:02,742 million for orders of magnitude, in the time elapsed from the microbackground 27 00:02:02,742 --> 00:02:07,157 release until then is of the order of half a billion years, so this is not an 28 00:02:07,157 --> 00:02:10,991 easy thing to achieve. And the question then is, how do we go 29 00:02:10,991 --> 00:02:15,410 from such small seeds of density fluctuations to the large density 30 00:02:15,410 --> 00:02:18,941 contrast that is observed in the objects that we see. 31 00:02:18,941 --> 00:02:22,744 Well here is a schematic flow chart of what has to happen. 32 00:02:22,744 --> 00:02:28,101 It begins with inflationary physics or very early [UNKNOWN] physics, which is 33 00:02:28,101 --> 00:02:32,482 not directly observable except as consequences of inflation. 34 00:02:32,482 --> 00:02:37,223 But then those fluctuations will grow and we see their imprint in microbackground 35 00:02:37,223 --> 00:02:41,747 even after microbackground is released, they do grow through gravitation and 36 00:02:41,747 --> 00:02:44,788 stability. The dense parts will attract more matter 37 00:02:44,788 --> 00:02:48,327 and become denser. That part is fairly easily understood and 38 00:02:48,327 --> 00:02:51,560 even modeled. It's Newtonian gravity because it's weak 39 00:02:51,560 --> 00:02:55,074 field. But, then gas falls into those potential 40 00:02:55,074 --> 00:02:59,118 wells, gets condensed, dissipates energy as it falls in. 41 00:02:59,118 --> 00:03:04,744 It makes stars, stars dump energy back, and those are very messy processes which 42 00:03:04,744 --> 00:03:09,699 have to be modeled hydrodynamically, and through radiative transfer. 43 00:03:09,699 --> 00:03:15,812 So, there is transitions from relatively simple, elegant, theoretical [UNKNOWN]. 44 00:03:15,812 --> 00:03:21,696 Geometry and gravitation into the really messy hydrodynamics radiation physics of 45 00:03:21,696 --> 00:03:26,212 what actually happens to the variance after the recombination. 46 00:03:26,212 --> 00:03:31,165 so let us set the stage for us. In the early universe, we know that it's 47 00:03:31,165 --> 00:03:34,963 very close to the critical matter dominated universe. 48 00:03:34,963 --> 00:03:38,621 Matter or radiation. And so, it's a very simple overall 49 00:03:38,621 --> 00:03:42,642 Friedmann equation. Regardless of what universe will evolve 50 00:03:42,642 --> 00:03:45,716 to later. Early on, its really close to a omega 51 00:03:45,716 --> 00:03:49,082 matter equal 1. And let's look at an over-dense region. 52 00:03:49,082 --> 00:03:52,348 Some were inside that exactly critical universe. 53 00:03:52,348 --> 00:03:56,192 It is essentially like little closed universe of its own. 54 00:03:56,192 --> 00:04:01,517 And initially, of course it expands, but, as you know, since its densities are 55 00:04:01,517 --> 00:04:06,742 greater than critical and surrounding universes are created also, overdense 56 00:04:06,742 --> 00:04:10,392 must be. that means that at some point, it'll have 57 00:04:10,392 --> 00:04:15,342 to turn around and fall back upon itself. So let's just subtract those two 58 00:04:15,342 --> 00:04:18,942 equations. And so that's, that's Friedmann equation 59 00:04:18,942 --> 00:04:23,197 for the difference in density, which we can simply rewrite as follows. 60 00:04:23,197 --> 00:04:27,837 So that's the difference of densities, but really we're looking at the density 61 00:04:27,837 --> 00:04:30,582 contrast. So, let's just divide it by the mean 62 00:04:30,582 --> 00:04:34,662 density, and so we'll call that as the overdense [UNKNOWN] delta, and its 63 00:04:34,662 --> 00:04:36,792 equation is shown here. Here. 64 00:04:36,792 --> 00:04:42,309 Now, since the density is inversely proportional to the scale factor. 65 00:04:42,309 --> 00:04:48,391 This is density of the matter, remember? So it just gets diluted as the cube of 66 00:04:48,391 --> 00:04:52,274 the radius. We see that the density contrast, the 67 00:04:52,274 --> 00:04:57,602 delta, will grow as the first power of the expansion factor, r of t. 68 00:04:57,602 --> 00:05:02,298 And we call that the era of the linear growth of perturbations. 69 00:05:02,298 --> 00:05:08,167 So between any two different redshifts, the change in the contrast will be given 70 00:05:08,167 --> 00:05:12,403 by the ratio of 1 plus redshift or rather the inverse thereof. 71 00:05:12,403 --> 00:05:19,338 So thet's try this from micro background roughly redshift 1000 to say first quasar 72 00:05:19,338 --> 00:05:25,317 roughly at redshift 5 or so. and we find out that the density contrast 73 00:05:25,317 --> 00:05:31,772 should have grown by a couple parts in thousands, whereas it should have been 74 00:05:31,772 --> 00:05:35,847 millions. So we were off by 9 orders of magnitude 75 00:05:35,847 --> 00:05:39,657 and clearly linear treatment does not apply. 76 00:05:39,657 --> 00:05:45,405 The solution to this is in part that, at the time of the micro background, the 77 00:05:45,405 --> 00:05:49,556 fluctuations that we see are those in varions and photons. 78 00:05:49,556 --> 00:05:54,770 But, underlying them are much deeper fluctuations in dark matter, and those 79 00:05:54,770 --> 00:05:59,112 have been growing since the universe became matter-dominated. 80 00:05:59,112 --> 00:06:03,951 So this is another reason why we think that dark matter must exist, because 81 00:06:03,951 --> 00:06:09,006 without it, we would simply not obtain the large-scale structure that we see. 82 00:06:09,006 --> 00:06:12,872 And that's a key idea. That the density fluctuations are 83 00:06:12,872 --> 00:06:17,972 dominated with the dark matter which, as you recall is several times more by 84 00:06:17,972 --> 00:06:22,747 density of regular bariums and those fluctuations grow even before the 85 00:06:22,747 --> 00:06:26,822 micro-background is released. So the fluctuations we see in 86 00:06:26,822 --> 00:06:32,636 micro-background are just little icing on the cake and after that Those variables 87 00:06:32,636 --> 00:06:39,265 can fall into those already preexisting potential wells built by the dark matter. 88 00:06:39,265 --> 00:06:44,194 Next time we will address this process in a little more detail.