1 00:00:00,012 --> 00:00:05,265 The existence of the cosmic microwave background is one of the two great 2 00:00:05,265 --> 00:00:11,423 predictions of the Big Bang cosmology. The other one is the nucleosynthesis of 3 00:00:11,423 --> 00:00:15,922 light elements. In the earlier stages of the expansion of 4 00:00:15,922 --> 00:00:21,791 the universe, there will be an equilibrium between electrons, positrons, 5 00:00:21,791 --> 00:00:25,609 protons, neutrons, and both species of neutrinos. 6 00:00:25,609 --> 00:00:30,695 And the reactions would work both ways and that lasts until the temperature 7 00:00:30,695 --> 00:00:35,683 drops to about 10 billion degrees or age of the universe about the second. 8 00:00:35,683 --> 00:00:40,720 And simply, because the neutron's are a little heavier, there will be fewer of 9 00:00:40,720 --> 00:00:44,247 them in the mix, which is why there will be asymmetry 10 00:00:44,247 --> 00:00:48,756 between them and protons. So their mass inequality causes asymmetry 11 00:00:48,756 --> 00:00:53,901 because of the beta decay and beta decay reactions that convert one into the 12 00:00:53,901 --> 00:00:56,900 other. It requires little less energy to turn 13 00:00:56,900 --> 00:01:01,972 neutron into a proton than the other way round, and so, that is the more favorite 14 00:01:01,972 --> 00:01:05,352 reaction. So after the annihilation of excess 15 00:01:05,352 --> 00:01:10,168 positrons, only neutrons can decay. We can again compute the ratio of 16 00:01:10,168 --> 00:01:15,550 neutrons and protons using Boltzmann's formula, and indeed, initially, at very 17 00:01:15,550 --> 00:01:20,470 high temperatures, there'd be slight asymmetry due to the reasons we just 18 00:01:20,470 --> 00:01:23,903 described. But the asymmetry increases as the 19 00:01:23,903 --> 00:01:28,993 universe expands and it finally gets frozen at the value of 0.227 when the 20 00:01:28,993 --> 00:01:34,266 universe is only 10^10 degrees hot. So that's how many neutrons come out of 21 00:01:34,266 --> 00:01:39,618 the equilibrium, but then they start decaying using in beta decay and have a 22 00:01:39,618 --> 00:01:43,052 mean lifetime of a little less than 15 minutes. 23 00:01:43,052 --> 00:01:48,883 So before they can be combined with protons into helium or other like nuclei, 24 00:01:48,883 --> 00:01:54,503 the decay destroys about 24, 25% of them. By the time temperature drops to a 25 00:01:54,503 --> 00:01:58,895 billion degrees, neutrons and protons can combine to form 26 00:01:58,895 --> 00:02:02,375 nuclei of helium according to these reactions. 27 00:02:02,375 --> 00:02:08,490 Some of those newly made nuclei of helium are then dissociated by residual photons, 28 00:02:08,490 --> 00:02:14,318 but as the universe expands, they cool it off and so no more association can occur. 29 00:02:14,318 --> 00:02:19,117 So by the time the universe is little less than 15 minutes old and the 30 00:02:19,117 --> 00:02:24,864 temperature drops to 300 million Kelvin, all of these ratios are frozen and those 31 00:02:24,864 --> 00:02:29,985 are the abundances that we will observe. Actually, the real network of reactions 32 00:02:29,985 --> 00:02:33,146 is a little more complicated and here it's shown. 33 00:02:33,146 --> 00:02:38,399 However the story we just went through pretty much captures the essence of it, 34 00:02:38,399 --> 00:02:42,817 but people who model cosmic nuclear synthesis have to actually do the 35 00:02:42,817 --> 00:02:47,657 full-blown reaction network. And the models predict how the abundances 36 00:02:47,657 --> 00:02:53,174 of different nuclear species will change in time as all this is going on as shown 37 00:02:53,174 --> 00:02:56,286 here. Now you can see that by the time it's all 38 00:02:56,286 --> 00:03:01,752 over, say 15 minutes after the Big Bang, the lines remain flat, except of course, 39 00:03:01,752 --> 00:03:05,772 for small residual number of neutrons that keep decaying. 40 00:03:05,772 --> 00:03:11,692 At this point, the neutron to proton ratio has dropped to 0.14 and these 41 00:03:11,692 --> 00:03:16,383 neutrons end up in the like nuclei that they're produced. 42 00:03:16,383 --> 00:03:22,144 This is roughly 25% by mass and this is why there's about 25% by mass of 43 00:03:22,144 --> 00:03:26,183 primordial helium. So in this way, the intrinsic mass 44 00:03:26,183 --> 00:03:31,240 difference between protons and neutrons, something that comes out of particle 45 00:03:31,240 --> 00:03:36,134 physics, determines the abundances of light nuclei created in the Big Bang. 46 00:03:36,134 --> 00:03:41,220 Since, essentially all neutrons are tied up in helium, its abundance is not 47 00:03:41,220 --> 00:03:44,712 dependent on density, but some of the other species, 48 00:03:44,712 --> 00:03:47,784 they do depend on the actual baryonic density. 49 00:03:47,784 --> 00:03:51,830 That the reason the reactions don't proceed beyond lithium or beryllium, 50 00:03:51,830 --> 00:03:57,119 beryllium or so is the universe expands and becomes insufficiently hot and dense 51 00:03:57,119 --> 00:04:01,927 to create heavier nuclei. Obviously, the heavier nuclei have higher 52 00:04:01,927 --> 00:04:06,256 charges and there is a higher Coulomb barrier to be overcome. 53 00:04:06,256 --> 00:04:11,554 So after helium, there is a big gap going to lithium, and then also another one 54 00:04:11,554 --> 00:04:16,382 going to boron, which is what limits the abundance of those elements. 55 00:04:16,382 --> 00:04:21,322 The Big Bang nucleosynthesis predicts abundances of light nuclei. 56 00:04:21,322 --> 00:04:26,753 And generally, this is parameterized as the ratio of the number of baryons to 57 00:04:26,753 --> 00:04:29,743 photons, which is frozen after all this is 58 00:04:29,743 --> 00:04:33,365 complete. Since there is roughly a billion photons 59 00:04:33,365 --> 00:04:37,378 for every baryon, usually 10^10 are units that are used 60 00:04:37,378 --> 00:04:40,630 here, and this ratio is closely related to the 61 00:04:40,630 --> 00:04:45,232 baryonic density according to the following simple formula. 62 00:04:45,232 --> 00:04:49,032 Since this ratio is preserved after all this is complete, 63 00:04:49,032 --> 00:04:53,142 we can measure it today and find out what it was in the early years, 64 00:04:53,142 --> 00:04:58,117 which leads to the prediction that Omega baryons will be of the order of 4% and 65 00:04:58,117 --> 00:05:02,872 that is in an excellent agreement with the completely different argument from 66 00:05:02,872 --> 00:05:07,722 micro background fluctuations. Here, the predictions of the Big Bang 67 00:05:07,722 --> 00:05:10,309 nucleosynthesis in plot it in one diagram. 68 00:05:10,309 --> 00:05:15,379 The different bands correspond to abundances of different nuclei at the end 69 00:05:15,379 --> 00:05:20,086 as a function of the baryon density. The steeper the line, the more it's 70 00:05:20,086 --> 00:05:25,150 sensitive to abundance of baryons. And you can see the deuterium will work 71 00:05:25,150 --> 00:05:29,593 best as a means of estimating the baryonic density in the universe. 72 00:05:29,593 --> 00:05:33,848 Helium-4 does not work at all because the line is essentially flat. 73 00:05:33,848 --> 00:05:38,930 The first confirmation of this is through measurement of the helium abundance. 74 00:05:38,930 --> 00:05:42,252 Star-forming galaxies are used for this purpose, 75 00:05:42,252 --> 00:05:51,873 and since stars synthesize helium as well as heavier elements, that should be in 76 00:05:51,873 --> 00:05:57,593 proportion. So by measuring abundance of other 77 00:05:57,593 --> 00:06:03,777 elements, say oxygen, and then correlating it with abundance of helium 78 00:06:03,777 --> 00:06:03,777 should be a line that goes through zero if there was no primordial helium 79 00:06:03,777 --> 00:06:06,870 created. However, because there was, then the 80 00:06:06,870 --> 00:06:11,772 intercept on the y-axis gives you the primordial abundance of helium. 81 00:06:11,772 --> 00:06:16,749 And that number is a little less than 24% is in an excellent agreement with 82 00:06:16,749 --> 00:06:20,069 predictions of the Big Bang nucleosynthesis. 83 00:06:20,069 --> 00:06:25,205 Remember that deuterium is the most sensitive one to the actual baryonic 84 00:06:25,205 --> 00:06:28,817 density. So, measuring cosmic abundance of the 85 00:06:28,817 --> 00:06:34,287 deuterium before it's processed in stars gives us a means of estimating the 86 00:06:34,287 --> 00:06:38,932 baryonic density of the universe. The way this is done is through 87 00:06:38,932 --> 00:06:44,621 absorption lines in spectra of quasars. The hydrogen clouds are called 88 00:06:44,621 --> 00:06:49,793 Lyman-alpha forest and there will be Lyman-alpha equivalent for deuterium 89 00:06:49,793 --> 00:06:55,292 line, because of its topic shift, its wave length will be little shorter than 90 00:06:55,292 --> 00:07:01,077 hydrogen Lyman-alpha. So the idea is to find clouds where there is enough of 91 00:07:01,077 --> 00:07:06,108 materials, so that the line is already, well saturated for hydrogen, but not 92 00:07:06,108 --> 00:07:10,508 enough to cover the equivalent absorption of the material. 93 00:07:10,508 --> 00:07:16,195 And of the order of dozens such systems have been measured, and from the relative 94 00:07:16,195 --> 00:07:21,525 abundance of the deuterium to hydrogen in these clouds, we can infer the baryonic 95 00:07:21,525 --> 00:07:25,909 density. Lithium is a little more complicated, 96 00:07:25,909 --> 00:07:30,840 because it's also generated in stars, and it's subject to uncertainties in stellar 97 00:07:30,840 --> 00:07:30,840 structure and evolution. And so this is why it's not really used 98 00:07:30,840 --> 00:07:35,477 to constrain, constrain nucleosynthesis. However, 99 00:07:35,477 --> 00:07:42,082 we note that its abundance is perfectly consistent with the predictions that 100 00:07:42,082 --> 00:07:47,222 satisfy the other measurements like helium and deuterium. 101 00:07:47,222 --> 00:07:51,820 And finally, all this also depends on the number of neutrino families, 102 00:07:51,820 --> 00:07:56,249 because that they each have degree of freedom in the early universe, 103 00:07:56,249 --> 00:08:01,567 and the Big Bang nucleosynthesis predicts that there should be only three of them, 104 00:08:01,567 --> 00:08:05,611 which is in agreement from what we know from particle physics. 105 00:08:05,611 --> 00:08:08,078 Next time, we'll talk about inflation.