1 00:00:00,012 --> 00:00:03,797 So, by the 1970s, say, after the discovery of the cosmic microwave 2 00:00:03,797 --> 00:00:08,400 background, the successes of Big Bang nucleosynthesis, doubts about whether the 3 00:00:08,400 --> 00:00:11,701 Big Bang was a real event had pretty much been dispelled. 4 00:00:11,701 --> 00:00:15,957 but the idea that we could actually make precission measurements of the 5 00:00:15,957 --> 00:00:18,500 cosmological parameters seemed far fetched. 6 00:00:18,500 --> 00:00:23,688 So, people played around with models, mostly based on their theoretical biases. 7 00:00:23,688 --> 00:00:27,622 the situation has changed drastically, the past few decades. 8 00:00:27,622 --> 00:00:32,783 And the first precision measurements of cosmological parameters were made by 9 00:00:32,783 --> 00:00:36,784 measuring the anisotropy of the cosmological microwave background. 10 00:00:36,784 --> 00:00:41,482 Remember, that in the 1990's, the COBE satillite produced the first 11 00:00:41,482 --> 00:00:46,631 anisotropy detected the motion of Earth through the cosmic microwave background. 12 00:00:46,631 --> 00:00:51,068 Subtracting that, you see that even absent Earth's motion, this is sort of 13 00:00:51,068 --> 00:00:55,455 taking into account Earth's motion, the microwave sky is not completely 14 00:00:55,455 --> 00:00:58,427 isotropic. This, remember, is the structure of the 15 00:00:58,427 --> 00:01:03,637 universe, this is telling us something about the way the universe was when it 16 00:01:03,637 --> 00:01:07,712 was 380,000 years old. This is the oldest light we're able to 17 00:01:07,712 --> 00:01:10,837 see. These are, if you want, the, a pattern of 18 00:01:10,837 --> 00:01:15,612 some inhomogenieties in the universe which hopefully later lead to the 19 00:01:15,612 --> 00:01:18,662 production of galaxies and clusters, and so on. 20 00:01:18,662 --> 00:01:22,752 Because the universe today is certainly not homogeneous. 21 00:01:22,752 --> 00:01:26,302 This was very exciting. We could learn a lot from it. 22 00:01:26,302 --> 00:01:31,127 In fact, a follow-up mission later renamed the Wilkinson Microwave 23 00:01:31,127 --> 00:01:36,502 Anisotropy Probe was launched and you can see that WMAP produced a far more 24 00:01:36,502 --> 00:01:41,727 detailed image of the sky. And what is it that we learned from these pictures? 25 00:01:41,727 --> 00:01:46,469 We see regions that are hotter and regions that are colder. 26 00:01:46,469 --> 00:01:52,513 What is it that we learn from this? Well, the first thing is again analysis 27 00:01:52,513 --> 00:01:58,264 of essentially the spectrum of, of fluctuations as a function of angular 28 00:01:58,264 --> 00:02:02,147 variation. So, over what angular ranges do does the, 29 00:02:02,147 --> 00:02:06,871 the temperature of the microwave background, what that maps is the effect 30 00:02:06,871 --> 00:02:12,909 of temperature, so there are regions of slightly hotter and slightly cooler. 31 00:02:12,909 --> 00:02:17,892 And the what we see is that large at angles above about a degree, there is 32 00:02:17,892 --> 00:02:23,142 very little correlative fluctuations, no large splotches are there in the galaxy. 33 00:02:23,142 --> 00:02:27,837 Of course, in the middle, that in the way. But at a range, at an angular size 34 00:02:27,837 --> 00:02:31,332 of about a degree, there is a large amount of fluctuation. 35 00:02:31,332 --> 00:02:36,237 And then, at about a third of a degree, and again at about a quarter of a degree, 36 00:02:36,237 --> 00:02:39,822 and to the less extent that about a tenth of a degree, 37 00:02:39,822 --> 00:02:44,493 there are smaller peaks. But, the, let's focus for a moment on this main peak, 38 00:02:44,493 --> 00:02:49,650 which is the dominant peak the dominant size of angular features of the microwave 39 00:02:49,650 --> 00:02:53,375 background as a degree. What does that tell me? Well, what is 40 00:02:53,375 --> 00:02:57,527 this? These are the images I claim of density, or sound waves in that 41 00:02:57,527 --> 00:03:02,263 primordial plasma at the age of 380,000 years after the Big Bang. 42 00:03:02,263 --> 00:03:07,754 how does this work? Well, you'd expect that there could be sound waves in the 43 00:03:07,754 --> 00:03:11,323 plasma, some region at by fluctuation becomes dense. 44 00:03:11,323 --> 00:03:14,765 It becomes hotter because of the compression. 45 00:03:14,765 --> 00:03:19,513 The heat generates radiation pressure that expands the region again, and you 46 00:03:19,513 --> 00:03:21,785 get this sort of oscillatory wave behavior. 47 00:03:21,785 --> 00:03:25,514 Two things to take into account. One is, all of this is dominated, these 48 00:03:25,514 --> 00:03:28,097 are, this plasma has gravitationally interacting. 49 00:03:28,097 --> 00:03:32,286 And it's responding to the gravitational pull of the much larger concentration of 50 00:03:32,286 --> 00:03:34,902 dark matter that is around. And the other thing is, 51 00:03:34,902 --> 00:03:39,389 that in fact, denser regions show up as colder in this map of the sky. 52 00:03:39,389 --> 00:03:44,463 The reason is indeed they were a little bit warmer, but this is overshadowed by 53 00:03:44,463 --> 00:03:49,566 something called the Sachs-Wolfe effect. Denser regions are deeper gravitational 54 00:03:49,566 --> 00:03:52,146 wells. The gravitational red shift of the 55 00:03:52,146 --> 00:03:56,848 photons emerging from these denser regions is larger than that from less 56 00:03:56,848 --> 00:04:00,901 dense regions. This overwhems the actual heating of the 57 00:04:00,901 --> 00:04:04,570 local region. So, in fact, the colder regions in the 58 00:04:04,570 --> 00:04:09,935 microwave sky represent denser regions. But, be that as it may, we are mapping 59 00:04:09,935 --> 00:04:15,656 essentially the density or temperature fluctuations of the universe at 380,000 60 00:04:15,656 --> 00:04:18,822 years and we're mapping these sound waves. 61 00:04:18,822 --> 00:04:23,639 Now, what do you expect the wavelength of these sound waves to be? Well, it turns 62 00:04:23,639 --> 00:04:28,791 out that we have a very good prediction for what the typical wavelength of such a 63 00:04:28,791 --> 00:04:32,885 sound wave would be. the typical wavelength, it turns out, is 64 00:04:32,885 --> 00:04:37,965 of the order of the distance sound can travel in that plasma in the time 380,000 65 00:04:37,965 --> 00:04:43,077 years that the universe has existed. Certainly, waves with wavelength larger 66 00:04:43,077 --> 00:04:48,493 than this should not exist because the wavelength basically, the, the size of a 67 00:04:48,493 --> 00:04:53,131 peak, a region that then coherently fluctuate to higher density without 68 00:04:53,131 --> 00:04:58,137 dissipating should be limited, just as we have in the past used the speed of light. 69 00:04:58,137 --> 00:05:02,281 Here, we're using the speed of sound to say that different regions can 70 00:05:02,281 --> 00:05:05,362 communicate with each other by the speed of sound. 71 00:05:05,362 --> 00:05:12,461 And this means that that wavelengths that you can expect should be smaller than or 72 00:05:12,461 --> 00:05:19,823 equal to, so smaller than or equal to the distance that sound could have traveled 73 00:05:19,823 --> 00:05:26,458 by that time in the age of the universe. Now, the speed of sound in this dense 74 00:05:26,458 --> 00:05:30,282 plasma is very high. It's 1 over square root. 75 00:05:30,282 --> 00:05:35,406 of 3 times the speed of light, because of the properties of strongly interacting 76 00:05:35,406 --> 00:05:41,475 plasma. And since we know the, distance that light could have traveled by this 77 00:05:41,475 --> 00:05:47,159 time, that is, the horizon distance wherein a matter dominated universe, 78 00:05:47,159 --> 00:05:54,387 we've we're talking about 380,000 years so it's after the 55,000 year radiation 79 00:05:54,387 --> 00:05:58,847 to matter domination. The horizon distance at time t, 80 00:05:58,847 --> 00:06:04,287 the distance light would have traveled since the big bang is 3*c*t. 81 00:06:04,287 --> 00:06:10,278 Since sound travels the square root of 3 1 over the squared of 3 times the speed 82 00:06:10,278 --> 00:06:13,560 of light, the wavelength we expect is 1 over square 83 00:06:13,560 --> 00:06:16,558 root of 3 times this, or this is our wave length. 84 00:06:16,558 --> 00:06:20,458 You can plug in the numbers, we know that time, 380,000 years. 85 00:06:20,458 --> 00:06:25,544 It turns out that we're talking about a wave length of about 201 kiloparsec. 86 00:06:25,544 --> 00:06:29,678 So, these are pretty long wave length oscillations in the plasma. 87 00:06:29,678 --> 00:06:34,500 Now, we are looking at this at a coordinate distance, this happened at 88 00:06:34,500 --> 00:06:39,766 some place. And the coordinate distance that light travels in the time from this 89 00:06:39,766 --> 00:06:44,959 time to our time. You can compute that using our understanding of the expansion 90 00:06:44,959 --> 00:06:48,629 of the universe. the distance time travels between t 91 00:06:48,629 --> 00:06:53,239 ionization and t0 is given by this expression it's this one third power. 92 00:06:53,239 --> 00:06:58,233 you can recognize at least that if I set t ionization to zero, the time that light 93 00:06:58,233 --> 00:07:03,461 has traveled since the Big Bang in this dust dominated universe is 3ct during 94 00:07:03,461 --> 00:07:08,002 this calculation requires an integral so I won't drag you through it. 95 00:07:08,002 --> 00:07:17,369 But, since we know that a(t) during the dust domainted era is given by 96 00:07:17,369 --> 00:07:26,417 a0*t/t0^2/3, I can replace t ionization over t0. 97 00:07:26,417 --> 00:07:32,635 And a0 is 1 by ionization to the 1/2 because I substitute to the power 1/3, to 98 00:07:32,635 --> 00:07:36,943 the power 3/2 to get 1/2. So, I get this expression for the 99 00:07:36,943 --> 00:07:40,831 coordinate distance. What is that? That is the distance today 100 00:07:40,831 --> 00:07:45,227 of the place from which we are seeing the cosmic microwave background. 101 00:07:45,227 --> 00:07:48,607 You can evaluate this and we will later find the number. 102 00:07:48,607 --> 00:07:53,497 But, for now, I want the expression. so what does this tell me? Well, what 103 00:07:53,497 --> 00:07:56,547 does this predict about? I have the wavelength. 104 00:07:56,547 --> 00:08:00,397 I have the distance. I want to predict the angular size in the 105 00:08:00,397 --> 00:08:02,087 sky, small angle formula. 106 00:08:02,087 --> 00:08:06,427 Let's use the small angle formula. I'm going to use the small angular 107 00:08:06,427 --> 00:08:10,586 formula, angle formula assuming the universe is 108 00:08:10,586 --> 00:08:17,869 flat, remembering that the angular size distance is coordinate distance, distance 109 00:08:17,869 --> 00:08:23,119 to date, divided by 1+z or multiplied by the scale factor. 110 00:08:23,119 --> 00:08:30,259 So, I plug in what I had. The coordinate distance is this. The ang, the wavelength 111 00:08:30,259 --> 00:08:34,675 is this. I, the redshift, 1 plus the redshift is 112 00:08:34,675 --> 00:08:40,157 the inverse of the scale factor. I evaluate this. 113 00:08:40,157 --> 00:08:47,103 The scale factor at ionization is 1100, plugin, you get 1 degree. 114 00:08:47,103 --> 00:08:53,850 So, what I have is that if I remember to apply the geometry of Friedmann, Roberts, 115 00:08:53,850 --> 00:09:01,880 and Walker and I assume that space is flat, I predict the correct angular size 116 00:09:01,880 --> 00:09:08,132 for these accoustic waves in the plasma. In other words, we have just proved the 117 00:09:08,132 --> 00:09:12,987 space is flat because remember what I used essentially in the small angle 118 00:09:12,987 --> 00:09:17,862 formula is the idea that geodesics are straight lines and triangles behave as 119 00:09:17,862 --> 00:09:21,052 they should. If the world, universe for example, had 120 00:09:21,052 --> 00:09:25,833 negative curvature, then the small angle formula would be ruined. 121 00:09:25,833 --> 00:09:31,784 Theta, as observed, would be smaller than a degree that you would predict from the 122 00:09:31,784 --> 00:09:37,029 flat universe for a given size. Whereas if the universe were positively 123 00:09:37,029 --> 00:09:42,463 curved, I would observe a large angle corresponding to the same triangle. 124 00:09:42,463 --> 00:09:48,310 And so, the fact that we obtain agreement is very strong evidence that space is 125 00:09:48,310 --> 00:09:51,747 flat. Here's this rather undramatic, because 126 00:09:51,747 --> 00:09:56,753 realistic representation of the triangle in a negatively curved. 127 00:09:56,753 --> 00:10:01,942 Or as they call it, open universe. And you would predict a smaller angle 128 00:10:01,942 --> 00:10:06,917 than the angle that we found. And so, when I said that I know that the 129 00:10:06,917 --> 00:10:12,267 universe is rather precisely flat, I have managed to draw a actual triangle 130 00:10:12,267 --> 00:10:16,942 whose base I know from other consideration, whose length I know from 131 00:10:16,942 --> 00:10:20,767 other consideration, compare to the small angle formula. 132 00:10:20,767 --> 00:10:26,612 And I have measured the curvature over a distance of about 16 billion light years. 133 00:10:26,612 --> 00:10:31,142 That's a pretty good base. So, I am constraining the curvature to be 134 00:10:31,142 --> 00:10:34,811 almost precisely zero. This is why we know space is flat. 135 00:10:34,811 --> 00:10:39,949 There is more structure obviously than just the first peak, there are these 136 00:10:39,949 --> 00:10:43,544 subsequent peaks at smaller angular distributions. 137 00:10:43,544 --> 00:10:48,877 First of all, there's the total absence of any fluctuations larger than a degree. 138 00:10:48,877 --> 00:10:52,088 This makes sense. We said fluctuations larger than this 139 00:10:52,088 --> 00:10:56,936 could not have formed because distinct regions within the same wave were outside 140 00:10:56,936 --> 00:11:01,356 each others particle horizon, could not have gotten together a coherent wave. 141 00:11:01,356 --> 00:11:06,329 understanding the subsequent peaks, you have to take into account, as I said, 142 00:11:06,329 --> 00:11:10,887 that the sound is sort of controlled by the density fluctuations of the dark 143 00:11:10,887 --> 00:11:14,412 matter. it turns out that the height and position 144 00:11:14,412 --> 00:11:18,142 of the second peak are sensitive to the baryonic dust density. 145 00:11:18,142 --> 00:11:22,507 The third peak, relative to the second peak, it's height and position are 146 00:11:22,507 --> 00:11:27,502 sensitive to the density of dark matter, that's a little bit technical for what 147 00:11:27,502 --> 00:11:31,982 we're doing. But, by combining observations of all the spectrum, we can 148 00:11:31,982 --> 00:11:38,077 learn information both about the total density, remember we have discovered that 149 00:11:38,077 --> 00:11:41,502 the universe is flat. So, omega is essentially one. 150 00:11:41,502 --> 00:11:46,877 a combi, that, that explains why I am so confident that omega, dark matter plus 151 00:11:46,877 --> 00:11:51,877 dark energy normal matter adds up to one plus radiation which is very small. 152 00:11:51,877 --> 00:11:57,786 And furthermore the ratio between dark matter and baryonic densities is further 153 00:11:57,786 --> 00:12:03,774 constrained by this measurement together with nuclear nucleosynthesis, we are 154 00:12:03,774 --> 00:12:08,146 beginning to get a handle on the precise values of these parameters. 155 00:12:08,146 --> 00:12:14,134 Lots more information can be extracted from this cosmic microwave background and 156 00:12:14,134 --> 00:12:19,766 is being extracted and more is constantly being done, polarization data analysis of 157 00:12:19,766 --> 00:12:24,053 the interaction of the background radiation with galaxy clusters. 158 00:12:24,053 --> 00:12:29,567 there is a lot of information and you can got to the WMAP project webpage and learn 159 00:12:29,567 --> 00:12:31,201 what else we can learn from.