1 00:00:00,012 --> 00:00:05,152 Let us now talk about what's often called the cosmic concordance. 2 00:00:05,152 --> 00:00:10,845 What's really meant by that is an agreement between all various methods, 3 00:00:10,845 --> 00:00:15,470 converging to the same values of cosmological parameters. 4 00:00:15,470 --> 00:00:19,429 Which, needless to say, never happened in the past. 5 00:00:20,928 --> 00:00:28,023 Usually, this is expressed in the diagram that plots omega matter on x axis and 6 00:00:28,023 --> 00:00:31,878 omega vacuum or omega lambda on the y axis. 7 00:00:31,878 --> 00:00:36,273 On that plane, flat universe is a straight line. 8 00:00:36,273 --> 00:00:39,712 a slope of -45 degrees. Because. 9 00:00:39,712 --> 00:00:43,055 The 2 always have to add up to 1 for a flat universe. 10 00:00:43,055 --> 00:00:48,054 Now, there are also models in which there is no big band, where cosmological 11 00:00:48,054 --> 00:00:52,198 constant is so large that it prevents the initial singularity. 12 00:00:52,198 --> 00:00:57,074 So, in this diagram we can plot error contours of different measurements. 13 00:00:57,074 --> 00:01:02,046 Cosmic microbackground 1 is an error elilipse nicely alligned with the flat 14 00:01:02,046 --> 00:01:06,478 universe line. The, supernovae Hubble diagram, is almost 15 00:01:06,478 --> 00:01:11,053 orthogonal to it. We can also make dynamical measurements, 16 00:01:11,053 --> 00:01:16,699 of omega mass, from clusters of galaxies, or from, by, barionic acoustic 17 00:01:16,699 --> 00:01:21,082 constellations, and those tend to be almost vertical. 18 00:01:21,082 --> 00:01:27,331 Mercifully, they all seem to converge and intersect at one place and that plat is 19 00:01:27,331 --> 00:01:32,398 on the flat universe line. This is where omega matter is a little 20 00:01:32,398 --> 00:01:36,436 less than 0.3 and omega vacuum is low more than 0.7. 21 00:01:36,436 --> 00:01:39,802 So remember if we look at supernova alone. 22 00:01:39,802 --> 00:01:45,467 They suggested there is a omega vacuum or cosmological constant. 23 00:01:45,467 --> 00:01:51,993 And, but it, by themselves alone do not tell you that universe is also flat. 24 00:01:51,993 --> 00:01:58,811 For the micro background alone we can certainly tell that universe by itself is 25 00:01:58,811 --> 00:02:05,632 flat but not how the omega matter and omega lambda are distributed although One 26 00:02:05,632 --> 00:02:09,122 can get probability distributions for those. 27 00:02:09,122 --> 00:02:15,447 If we then add measurements from large scale structure which probe the dynamics 28 00:02:15,447 --> 00:02:19,242 then altogether they intersect in the same place. 29 00:02:19,242 --> 00:02:23,772 And so the point is, that various methods of measurement. 30 00:02:23,772 --> 00:02:28,759 Completely different methods of measurement converge to the same thing, 31 00:02:28,759 --> 00:02:34,277 which is what gives us some faith that indeed these are correct interpretations, 32 00:02:34,277 --> 00:02:39,036 that we do have finally measurements of the cosmological parameters. 33 00:02:39,036 --> 00:02:44,391 Note, however, that in most tests. There is a degeneracy between parameters. 34 00:02:44,391 --> 00:02:49,601 You can trade one for the other a little bit in the particular direction in this 35 00:02:49,601 --> 00:02:54,563 parameter space, so in cosmic micro background, that's fairly obvious that 36 00:02:54,563 --> 00:02:57,649 there are all these elongated error ellipsis. 37 00:02:57,649 --> 00:03:02,990 And generally speaking, for any one of these tests, you get probability dance 38 00:03:02,990 --> 00:03:06,369 the contours in some sort of parameter space. 39 00:03:06,369 --> 00:03:11,716 And there is a best fit father, but that need not be the be the actual best 40 00:03:11,716 --> 00:03:14,763 answer. And somehow, and product of this 41 00:03:14,763 --> 00:03:20,093 probability, clouds, has to really converge to the most likely over all 42 00:03:20,093 --> 00:03:24,288 value of the parameters. Generally this is done through basen/g 43 00:03:24,288 --> 00:03:28,506 statistical approach, especially for the micro background measurements. 44 00:03:28,506 --> 00:03:32,638 It involves a lot of computations and Monte Carlo simulations, but it's a 45 00:03:32,638 --> 00:03:37,228 process that's well understood. Also if you can declare values of some 46 00:03:37,228 --> 00:03:42,418 parameters now, it immediately narrows down probability distributions for 47 00:03:42,418 --> 00:03:45,708 others. For example you can take value of hubble 48 00:03:45,708 --> 00:03:51,099 constant just derived from hubble key project, and fix that and then get better 49 00:03:51,099 --> 00:03:57,094 answers for the omegas, So, here is an example of probability distributions for 50 00:03:57,094 --> 00:04:02,074 various parameters from a a paper by Tegmark et al that includes all of these 51 00:04:02,074 --> 00:04:06,312 data together. And you can see that, for most of them. 52 00:04:06,312 --> 00:04:11,275 What's obtained is not a sharp value of a parameter, but rather an extended 53 00:04:11,275 --> 00:04:14,879 distribution. You can then project these probability 54 00:04:14,879 --> 00:04:18,779 density distributions in various parameter space planes. 55 00:04:18,779 --> 00:04:23,989 And, for example, here is one that shows Hubble constant expressed as little h 56 00:04:23,989 --> 00:04:28,794 versus omega of matter. The big red regions are regions that are 57 00:04:28,794 --> 00:04:35,419 excluded using WMAP observations alone. Then the other sources of measurement 58 00:04:35,419 --> 00:04:41,565 like Hubble Space Telescope and Zone intersect and you find out that indeed, 59 00:04:41,565 --> 00:04:46,602 all of the probability distributions peak out at one common value. 60 00:04:46,602 --> 00:04:51,937 It's not a sharp value for sure, but it's a much narrower distribution than 61 00:04:51,937 --> 00:04:55,972 otherwise would be. And here is our concordance plot now 62 00:04:55,972 --> 00:05:00,937 shown a little differently. The red regions again are excluded by the 63 00:05:00,937 --> 00:05:05,372 WMAP measurements alone. The orange regions by there in crude 64 00:05:05,372 --> 00:05:11,463 analysis, if they add Measurements from large scale structure from Sloan Digital 65 00:05:11,463 --> 00:05:14,953 sky survey. Then that goes further down and then 66 00:05:14,953 --> 00:05:20,356 finally they also use supernova narrows the arrow's ellipse right around a 67 00:05:20,356 --> 00:05:26,042 magical set of values, of .7 and .3. Here is another one where Hubble Constant 68 00:05:26,042 --> 00:05:31,264 is plotted against total omega. Total omega seems to converge to unity in 69 00:05:31,264 --> 00:05:36,901 the resist flat with Hubble Constant again having the same range of values as 70 00:05:36,901 --> 00:05:41,235 we've seen before. Or one can ask the question, in terms of 71 00:05:41,235 --> 00:05:46,067 the age of the universe and omegas and here we have plot that shows error 72 00:05:46,067 --> 00:05:50,495 contrast of this, so. Different colors, remember, respond to 73 00:05:50,495 --> 00:05:54,101 introduction of evermore obsvervational constraints. 74 00:05:54,101 --> 00:05:59,206 Red, from just original w map data alone, orange for better analysis, yellow, 75 00:05:59,206 --> 00:06:03,592 including large scale structure and finally, using supernovae. 76 00:06:03,592 --> 00:06:09,738 Now recall the equation of state paraeter w for pure cosmological constant that is 77 00:06:09,738 --> 00:06:13,986 exactly minus one. Series the plot of error counters of w 78 00:06:13,986 --> 00:06:20,275 against omega and there is a fairly broad distribution thats allowed but subsequent 79 00:06:20,275 --> 00:06:24,152 measurements got that narrowed down to minus one. 80 00:06:24,152 --> 00:06:29,251 Another quantity that can be estimated is the number of neutrino species. 81 00:06:29,251 --> 00:06:35,018 intrestingly enough, because neutrino do contribute to energy lasting universe in 82 00:06:35,018 --> 00:06:40,346 a similar way that protons do so here is a gamble that concordance plug with as 83 00:06:40,346 --> 00:06:45,977 shown earlier, various methods together. Make estimate circle's more larger 84 00:06:45,977 --> 00:06:51,447 parameters sharper, and they always do all converge to the same set of values. 85 00:06:51,447 --> 00:06:56,864 Alpha omega matter, a little less than 0.03 and omega vacuum or omega landa, a 86 00:06:56,864 --> 00:07:01,139 little more than 0.07. A great deal was made out of this as the 87 00:07:01,139 --> 00:07:06,202 discovery of dark energy, but. This is perhaps overstating things a bit. 88 00:07:06,202 --> 00:07:11,135 Cosmological constants been with us for a long time now and astronomers have 89 00:07:11,135 --> 00:07:15,467 considered it seriously to explain more or less the same problems. 90 00:07:15,467 --> 00:07:20,018 And here's for example a title page from a paper in nature by two famous 91 00:07:20,018 --> 00:07:23,372 astronomers, James Gunn, and Beatrice Tinsley. 92 00:07:23,372 --> 00:07:28,857 They introduce cosmological constant for more or less the same reasons, 93 00:07:28,857 --> 00:07:34,707 astronomers invoked it later in 1990's to reconcile what, otherwise would be 94 00:07:34,707 --> 00:07:39,352 discrepant measurements of Hubble Constant and the density. 95 00:07:39,352 --> 00:07:45,695 Here is a simple concordance diagram I myself made as a graduate student of 30 96 00:07:45,695 --> 00:07:49,327 years before the supernova results were announced. 97 00:07:49,327 --> 00:07:52,956 We didn't have a supernova a Hubble diagram then. 98 00:07:52,956 --> 00:07:58,270 But one could use lines of equal age of these models and choose the set that's 99 00:07:58,270 --> 00:08:03,612 roughly what globular clusters gave you and that turns what out works just as 100 00:08:03,612 --> 00:08:07,344 well as supernova. So that too pointed out that if you 101 00:08:07,344 --> 00:08:11,181 wanted. A flat universe say, demanded by the 102 00:08:11,181 --> 00:08:17,308 inflation theory, then, you must accept solution where by, density is really only 103 00:08:17,308 --> 00:08:21,401 around 0.3, and, cosmological constant is around 0.7. 104 00:08:21,401 --> 00:08:26,781 So to recap, our best guess universe parameters today, is that the age is 105 00:08:26,781 --> 00:08:31,826 about 13.7 billion years. The Hubble constant is just a tad over 70 106 00:08:31,826 --> 00:08:37,820 kilometers per second per megaparsec. The density of variance, normal matter as 107 00:08:37,820 --> 00:08:43,308 we know it, is around 4% or 4 1/2%. That the total matter density including 108 00:08:43,308 --> 00:08:49,173 the dark matter, which is not barionic, is about 0.27 and the energy density 109 00:08:49,173 --> 00:08:55,729 corresponding to the dark energy possibly cosmological constant it makes up the 110 00:08:55,729 --> 00:09:00,403 rest of about 0.73. So let's just look at 3 key densities, 111 00:09:00,403 --> 00:09:06,474 the total density again expressed as fractional critical density which is 112 00:09:06,474 --> 00:09:09,882 close to 1. The matter density and the baryonic 113 00:09:09,882 --> 00:09:13,682 matter density. Interestingly enough, if we just add up 114 00:09:13,682 --> 00:09:19,032 all the luminous matter that we see in galaxies, stars, radio emission from gas 115 00:09:19,032 --> 00:09:22,357 and so on. That only adds to like half a percent of 116 00:09:22,357 --> 00:09:26,157 the critical density. Much less than the total number of 117 00:09:26,157 --> 00:09:30,768 variants that we know. And so because 0.5% is less than about 118 00:09:30,768 --> 00:09:36,267 4%, there has to be some sort of missing baryonic matter, and that was an 119 00:09:36,267 --> 00:09:42,343 interesting problem in of itself, and because 0.04 is less than 0.27, there has 120 00:09:42,343 --> 00:09:47,606 to be a non-baryonic component of matter. Which is the dark matter. 121 00:09:47,606 --> 00:09:53,566 And because .27 is less than 1, there has to be dark energy in order to fill up the 122 00:09:53,566 --> 00:09:56,731 rest. So to recap the cosmological tests. 123 00:09:56,731 --> 00:10:02,793 They always based on comparing some kind of measure of distance versus redshift. 124 00:10:02,793 --> 00:10:07,672 And in order to do this we use test particles of different kinds. 125 00:10:07,672 --> 00:10:12,222 If we have objects of ostensibly co-luminosity, those are standard 126 00:10:12,222 --> 00:10:15,372 candles. If we have objects of ostensible same 127 00:10:15,372 --> 00:10:20,397 size, those are standard rulers. And if we have a standard population that 128 00:10:20,397 --> 00:10:24,947 fills up the universe, say, galaxy clusters, then we have standard 129 00:10:24,947 --> 00:10:28,122 population. In addition to these cosmological 130 00:10:28,122 --> 00:10:34,407 observations, we also obtain measurements of the omega matter from local dynamics 131 00:10:34,407 --> 00:10:38,697 or large scale structure. We can then combine that with independent 132 00:10:38,697 --> 00:10:43,757 measurements of Hubble constant, through the distance ladder process we talked 133 00:10:43,757 --> 00:10:47,087 about earlier. Or ages of globular clusters that can 134 00:10:47,087 --> 00:10:51,250 find age of the universe. And so, even though there are many 135 00:10:51,250 --> 00:10:56,946 couplings and degeneracies for any given method between different parameters, all 136 00:10:56,946 --> 00:10:59,856 of them converge to the same set of values. 137 00:10:59,856 --> 00:11:03,829 Because of this we believe that we have a good picture now. 138 00:11:03,829 --> 00:11:08,639 Many different methods, completely different kinds of measurements, 139 00:11:08,639 --> 00:11:13,880 completely different kinds of physics. All converts to the same thing and this 140 00:11:13,880 --> 00:11:18,596 is why we think that concordance cosmology is now fairly well-established. 141 00:11:18,596 --> 00:11:22,077 Next time, we'll start talking about the early universe.