1 00:00:00,012 --> 00:00:06,812 We now turn, to the use of the cosmic microwave background, as a cosmological 2 00:00:06,812 --> 00:00:10,787 tool. This turns out to be, the most powerful 3 00:00:10,787 --> 00:00:16,662 tool in our arsenal today. And it's what really led us into the era 4 00:00:16,662 --> 00:00:21,985 of precision cosmology. The basic idea is as follows If we had 5 00:00:21,985 --> 00:00:27,515 something sufficiently large in the early universe that can be measured and we knew 6 00:00:27,515 --> 00:00:33,021 what redshift it was, then we could apply angular diameter test to it and constrain 7 00:00:33,021 --> 00:00:38,526 cosmological parameters from that and the largest possible thing we could think of 8 00:00:38,526 --> 00:00:43,880 would be The particle horizon at the time, which is the distance out to which 9 00:00:43,880 --> 00:00:49,222 causal connection can be established at the time that universe was that old. 10 00:00:49,222 --> 00:00:54,740 If we can infer the size of the particle horizon from physical reasons And, if we 11 00:00:54,740 --> 00:00:59,324 can somehow find its signature, in the microwave background, then we can perform 12 00:00:59,324 --> 00:01:02,075 the test. There will be density fluctuations, in 13 00:01:02,075 --> 00:01:06,512 the early universe, and those that are leftover from the quantum fluctuations, 14 00:01:06,512 --> 00:01:09,679 from even earlier times, in the history of the universe. 15 00:01:09,679 --> 00:01:13,672 And they would manifest themselves as slight variations in density. 16 00:01:13,672 --> 00:01:18,848 You can decompose those in series of waves overlapping and the matter would 17 00:01:18,848 --> 00:01:23,691 fall towards the densest parts and because the matter and radiation are 18 00:01:23,691 --> 00:01:29,252 tightly coupled before the micro backend was released, radiation would follow, 19 00:01:29,252 --> 00:01:33,712 inducing some slight Doppler shifts in its thermal emission. 20 00:01:33,712 --> 00:01:37,987 So when, microwave background is released, the decoupling stops, and, 21 00:01:37,987 --> 00:01:43,921 whatever pattern of fluctuation was there will remain frozen and observable today. 22 00:01:43,921 --> 00:01:49,248 Theory predicts that those who have amplitudes of some, parts in million of 23 00:01:49,248 --> 00:01:54,783 the present-day temperature, which is 2.7 degree Kelvin, and so be very, very 24 00:01:54,783 --> 00:01:59,481 subtle effect to measure. So for a long time, cosmologists tried to 25 00:01:59,481 --> 00:02:03,430 measure these fluctuations, and finally they succeeded. 26 00:02:03,430 --> 00:02:08,619 There have been many experiments leading towards this, but the first really 27 00:02:08,619 --> 00:02:14,722 successful one, was a balloon born, micro background, measurement, from Antarctica 28 00:02:14,722 --> 00:02:18,735 called Boomerang. It was led by Andrew Lange and Paolo de 29 00:02:18,735 --> 00:02:24,586 Bernardis, and they were the first ones to have convincing measurement of this 30 00:02:24,586 --> 00:02:29,597 fluctuation at the scales that are relevant here, and the first ones to 31 00:02:29,597 --> 00:02:33,342 actually infer cosmological parameters from that. 32 00:02:33,342 --> 00:02:38,514 This was probably the single most important measurement at the time. 33 00:02:38,514 --> 00:02:44,626 At about the same time as the supernovae yielded the evidence for dark energy, and 34 00:02:44,626 --> 00:02:49,244 together they really opened this era of precision cosmology. 35 00:02:49,244 --> 00:02:55,424 Subsequently, WMAP satellite, which is Wilkinson Microwave Anisotropy Probe was 36 00:02:55,424 --> 00:03:01,041 launched And its purpose was to do this measurement even more precisely, and 37 00:03:01,041 --> 00:03:06,077 today the best results we have come from analysis of the data from WMAP. 38 00:03:06,077 --> 00:03:10,244 So here's how this works. If you were to take an image of the 39 00:03:10,244 --> 00:03:16,044 cosmic microwave background, it will be pretty uniform and so you have to turn 40 00:03:16,044 --> 00:03:22,037 the contrast now by factor of 1000. And then, you see that there is a dipole, 41 00:03:22,037 --> 00:03:27,435 due to the motion of the Milky Way relative to microwave background. 42 00:03:27,435 --> 00:03:33,615 If we then subtract dipole, and then turned a knob to even higher contrast to 43 00:03:33,615 --> 00:03:40,117 a million then we'll see fluctuations in the sky, a lot of them associated with 44 00:03:40,117 --> 00:03:46,341 the Milky Way galaxy, the foreground emission from synchrotron and dust and so 45 00:03:46,341 --> 00:03:52,877 on and after careful modelling which is very difficult and very delicate emission 46 00:03:52,877 --> 00:03:57,323 from the galaxy has to be removed and what's left is a pattern of density 47 00:03:57,323 --> 00:04:02,177 fluctuations in the early universe that have cosmological origin and that is the 48 00:04:02,177 --> 00:04:06,046 signal we're looking for. So here is an image which is from the 49 00:04:06,046 --> 00:04:10,643 boomerang measurement, it's a false color representation of temperature 50 00:04:10,643 --> 00:04:14,343 fluctuations in the sky. And you can see that they're 51 00:04:14,343 --> 00:04:18,672 characteristic size blobs, they turn out to be about 1 degree. 52 00:04:18,672 --> 00:04:23,923 So that is actually size of the particle horizon at the time of the coupling. 53 00:04:23,923 --> 00:04:29,097 So here again is how this works, in the early universe there will be density 54 00:04:29,097 --> 00:04:32,502 fluctuations as residual of quantum processes. 55 00:04:32,502 --> 00:04:38,497 Matter will be falling toward the densest parts, radiation will follow and have 56 00:04:38,497 --> 00:04:44,697 slight Doppler shifts, this is why things are called Doppler peaks later. 57 00:04:44,697 --> 00:04:49,112 And when the coupling time comes the pattern is frozen. 58 00:04:49,112 --> 00:04:54,592 If you now remember Fourier decomposition and in density field. 59 00:04:54,592 --> 00:04:59,657 In any number of dimensions, whether it's a straight line, like normal acoustic 60 00:04:59,657 --> 00:05:04,652 signals, or three dimensional field and density, can be decomposed into set of 61 00:05:04,652 --> 00:05:08,172 overlapping waves. And the largest one of those, is the 62 00:05:08,172 --> 00:05:12,537 largest wave of them that can be accomodated, which is the size of the 63 00:05:12,537 --> 00:05:16,312 particle horizon. The pattern will then stay imprinted, on 64 00:05:16,312 --> 00:05:21,099 the micro background radiation. After it's been decoupled from the 65 00:05:21,099 --> 00:05:26,836 matter, and by measuring it we can infer things about size of the horizon, and 66 00:05:26,836 --> 00:05:32,274 expansion rate at the time it was released, and it depends actually in all 67 00:05:32,274 --> 00:05:38,122 manner of cosmological parameters, which can be computed nicely from theory. 68 00:05:38,122 --> 00:05:44,123 The way we quantify this is through spherical harmonics, which is essentially 69 00:05:44,123 --> 00:05:50,887 in equivalent of Fourier decomposition on a sphere, schematically this is how it 70 00:05:50,887 --> 00:05:56,741 works, just like in Fourier analysis, fluctuations of certain size would be 71 00:05:56,741 --> 00:06:02,042 represented as a, peak in the power spectrum, for responding to that spatial 72 00:06:02,042 --> 00:06:05,086 wavelength. The big ones, would have, very low 73 00:06:05,086 --> 00:06:08,865 spatial frequency. The small ones would have very high 74 00:06:08,865 --> 00:06:12,878 spatial frequency. Here is a simple mathematical, simulation 75 00:06:12,878 --> 00:06:14,562 of this from N. Wright. 76 00:06:14,562 --> 00:06:20,432 Putting different numbers of waves on a sphere, corresponding to a different wave 77 00:06:20,432 --> 00:06:24,782 number, which is called l. Mathematically, this is, again, 78 00:06:24,782 --> 00:06:28,852 equivalent to Fourier decomposition, but on a sphere. 79 00:06:28,852 --> 00:06:34,584 And instead of fewer components, we are talking about spherical harmonics and any 80 00:06:34,584 --> 00:06:39,639 signal on the surface of the sphere can be expressed as a sum of spherical 81 00:06:39,639 --> 00:06:45,243 harmonics weighted properly component by component and formulas for each one of 82 00:06:45,243 --> 00:06:49,836 those exist and can be it computed. So what's measured, really, is a 83 00:06:49,836 --> 00:06:54,765 combination, of many different waves, but different wavelengths, on the sphere, 84 00:06:54,765 --> 00:06:58,761 have different weights. And, their distribution will be the power 85 00:06:58,761 --> 00:07:01,890 spectrum. So again, this was completely equivalent 86 00:07:01,890 --> 00:07:06,382 to power spectra in, Fourier analysis, except that now their waves are in a 87 00:07:06,382 --> 00:07:11,495 sphere, and no a line, or, in a plane. So from the measurements we can infer 88 00:07:11,495 --> 00:07:17,174 what the power spectrum is and from that we can then infer something about initial 89 00:07:17,174 --> 00:07:21,664 density fluctuations. he characteristic size that corresponds 90 00:07:21,664 --> 00:07:27,343 to particle horizon of the time is given by the wave number is equal approximately 91 00:07:27,343 --> 00:07:32,741 180 degrees divided by that Spherical harmonic l and if we can find out what 92 00:07:32,741 --> 00:07:38,487 that is then we can say something about size and expansion rate of the unaries at 93 00:07:38,487 --> 00:07:44,345 that time.So here WMAP results, interim results they got a slightly better later 94 00:07:44,345 --> 00:07:49,636 as they kept reducing delay time and there is a very prominent and obvious 95 00:07:49,636 --> 00:07:53,908 peak at about. L of 200, or angular scale a little less 96 00:07:53,908 --> 00:07:59,010 than one degree, and that corresponds to the size of the horizon. 97 00:07:59,010 --> 00:08:03,710 The other bumps you see are harmonics of the base frequency. 98 00:08:03,710 --> 00:08:10,111 So different cosmological models in different combinations of parameters Make 99 00:08:10,111 --> 00:08:15,508 a prediction of a pair that will go through these data points and shown here 100 00:08:15,508 --> 00:08:21,528 is a particularly well fitting model that is model that's now pretty much generally 101 00:08:21,528 --> 00:08:25,130 accepted. The exact positions and amplitudes and 102 00:08:25,130 --> 00:08:29,132 relative amplitudes and widths of these peaks depend. 103 00:08:29,132 --> 00:08:34,447 Again, on complicated mi-, mixtures of cosmological parameters. 104 00:08:34,447 --> 00:08:40,327 Total matter density, dark energy density, baryonic density, expansion 105 00:08:40,327 --> 00:08:44,252 rate, and so on. And in principle could be used to 106 00:08:44,252 --> 00:08:48,962 constrain all of it. However this is a very complex process 107 00:08:48,962 --> 00:08:55,358 and analysis involves creating large ensembles of Model universes and finding 108 00:08:55,358 --> 00:09:01,835 out which fit best and what are, what are the likelihood distributions of each 1 of 109 00:09:01,835 --> 00:09:07,550 the parameters So the 1st question was, what is the basic geometry of the 110 00:09:07,550 --> 00:09:12,442 universe? Is it open, closed or just critical? And in fact. 111 00:09:12,442 --> 00:09:16,673 It turns out it was flat within the measurement errors. 112 00:09:16,673 --> 00:09:22,835 That initial measurement, so that omega total is within 1 sigma away from unity. 113 00:09:22,835 --> 00:09:29,155 So even the original measurement implied that universe is flat within measurement 114 00:09:29,155 --> 00:09:33,067 errors, which are of the order of a couple percent. 115 00:09:33,067 --> 00:09:39,767 Since then, this got even more precise. That in itself is a very important 116 00:09:39,767 --> 00:09:42,721 result. The universe is spacially flat. 117 00:09:42,721 --> 00:09:48,386 But remember, it, that can be achieved as a many different combinations of the 118 00:09:48,386 --> 00:09:53,639 density of matter and density of, dark energy or cosmological constant. 119 00:09:53,639 --> 00:09:59,011 So by itself this measurement doesn't tell you much about the dark energy. 120 00:09:59,011 --> 00:10:04,059 But combined with others it can be used as a very powerful constraint. 121 00:10:04,059 --> 00:10:09,481 So, for example, if we can deduce from dynamical measurements that the Ω of 122 00:10:09,481 --> 00:10:15,467 mater is about 0.3 then this immediately implies that Ω of the dark energy is but 123 00:10:15,467 --> 00:10:18,687 0.7. Or if we can combine it with another 124 00:10:18,687 --> 00:10:24,282 measurement, like that one of supernovi. That will do the same thing. 125 00:10:24,282 --> 00:10:30,187 It's important to note that since so many parameters are mixed together in 126 00:10:30,187 --> 00:10:34,322 producing these patterns of density fluctuations. 127 00:10:34,322 --> 00:10:39,773 There's some degeneracy which means essentially that lot of them 128 00:10:39,773 --> 00:10:45,642 will be coupled together and in this particular case error ellipses are highly 129 00:10:45,642 --> 00:10:51,620 elongated along the line that's almost parallel to the flat universe line in the 130 00:10:51,620 --> 00:10:55,312 old diagram of omega matter versus omega vacuum. 131 00:10:55,312 --> 00:11:00,064 Which is why we think the universe is very close to flat so that degeneracy can 132 00:11:00,064 --> 00:11:05,081 be broken by a different measurement which would have error ellipses that are 133 00:11:05,081 --> 00:11:09,511 not oriented in the same way and you may recall that those from supernova 134 00:11:09,511 --> 00:11:12,517 measurements looked pretty much orthogonal through this. 135 00:11:12,517 --> 00:11:15,732 Another important measurement comes out of this, 136 00:11:15,732 --> 00:11:20,262 is how many baryons are there in the universe? The more matter there is, 137 00:11:20,262 --> 00:11:25,442 stronger fluctuations, and therefore the amplitudes of the peaks will be higher. 138 00:11:25,442 --> 00:11:30,297 So here are examples of 2 models with, different amounts of Baryonic matter. 139 00:11:30,297 --> 00:11:36,130 And by fitting to the actual data we can infer omega baryons. And the result is 140 00:11:36,130 --> 00:11:41,774 shown here, expressed in units of h which is Hubble constant units of 100 141 00:11:41,774 --> 00:11:47,570 kilometers per second per mega-parsec since we know h is roughly point 7, then 142 00:11:47,570 --> 00:11:50,722 this really means the mega-variance is about 4.5%. 143 00:11:52,075 --> 00:11:56,729 And this is in remarkably good agreement. With a measurement from cosmic 144 00:11:56,729 --> 00:12:01,201 nucleosynthesis, that we will come to later, which is, completely independent, 145 00:12:01,201 --> 00:12:05,327 assumes different physics, different measurements and different everything, 146 00:12:05,327 --> 00:12:09,407 which is why we believe that this result is probably correct, because when you 147 00:12:09,407 --> 00:12:13,109 have different. Matters leading to the same, result, 148 00:12:13,109 --> 00:12:18,718 then, that gives us, much more credence. So the question then arises, alright if 149 00:12:18,718 --> 00:12:23,228 there were these characteristic fluctuations, at the time of the 150 00:12:23,228 --> 00:12:27,761 coupling, will the be observable later on? And the answer is yes. 151 00:12:27,761 --> 00:12:33,064 There will be, corresponding imprint, on a very large scale structure in the 152 00:12:33,064 --> 00:12:37,682 universe. Which could be observable in principle in 153 00:12:37,682 --> 00:12:44,491 clustering of galaxies at comparable scales which are roughly hundred twenty 154 00:12:44,491 --> 00:12:49,890 mega par secs for the age of one for two hundred mega par secs for realistic 155 00:12:49,890 --> 00:12:55,495 values of Hubble constant. Hints of these were seen first, Redshift 156 00:12:55,495 --> 00:13:01,965 survey from Australia, the 2DF, redshift survey which we'll address later. 157 00:13:01,965 --> 00:13:07,955 And then confirmed, with Sloan Digital Sky Survey, there is a slight excess of 158 00:13:07,955 --> 00:13:13,981 power in clustering of galaxies on the scales that correspond now to that first 159 00:13:13,981 --> 00:13:19,542 Doppler The peak, except this is much later in the history of the universe. 160 00:13:19,542 --> 00:13:24,995 So the same standard ruler is now observed at different redshifts, and that 161 00:13:24,995 --> 00:13:30,473 makes the test far more powerful. Essentially, what that means is the error 162 00:13:30,473 --> 00:13:36,262 ellipses now rotate, and from multiple measurements, you can deduce A lot about, 163 00:13:36,262 --> 00:13:41,586 geometry, even without re, resorts, to the other measurements like supernovae. 164 00:13:41,586 --> 00:13:45,154 Now there are, many efforts, aimed to do precisely this. 165 00:13:45,154 --> 00:13:49,594 To observe the slight excess of clustering, corresponding to the first 166 00:13:49,594 --> 00:13:53,689 Doppler peak in microwave background, at the range of redshifts. 167 00:13:53,689 --> 00:13:57,762 And that can constrain cosmological perameters even better. 168 00:13:57,762 --> 00:14:02,688 Here is a table, from some of the cosmological parameters, many of which we 169 00:14:02,688 --> 00:14:06,905 haven't introduced yet, having to do with structure formation. 170 00:14:06,905 --> 00:14:11,562 Just as an illustration of the precision, that was obtained from WMAP. 171 00:14:11,562 --> 00:14:16,042 It actually got even better. this was after 3 years, of data. 172 00:14:16,042 --> 00:14:21,434 And now we have final results that after 9 years of data which is very slightly 173 00:14:21,434 --> 00:14:25,350 different and more precise even better data are coming. 174 00:14:25,350 --> 00:14:32,327 ESA has a satellite called plank which is essentially like WMAP with even a higher 175 00:14:32,327 --> 00:14:38,073 precision, and we expect to see results from that within a year or thereabouts. 176 00:14:38,073 --> 00:14:42,654 Next time, we will address source counts as a cosmological test