1 00:00:00,012 --> 00:00:03,925 So, we can take a measure of the temperature of the universe and we have 2 00:00:03,925 --> 00:00:07,799 really good evidence that the universe is isotropic and homogeneous. 3 00:00:07,799 --> 00:00:12,164 We'll see that we learn a lot more from the cosmic background in the 2000s than 4 00:00:12,164 --> 00:00:16,224 just that it exists but that's not evidence, what I've given you so far is 5 00:00:16,224 --> 00:00:18,828 far from convincing evidence for the Big Bang. 6 00:00:18,828 --> 00:00:23,282 Some of the best evidence for the Big Bang is a story that is rarely told and 7 00:00:23,282 --> 00:00:28,184 is, because it's a bit technical, but I want to tell it and I want I think we can 8 00:00:28,184 --> 00:00:32,163 appreciate what's going on. So, you know this is the story of Big 9 00:00:32,163 --> 00:00:37,402 Bang nucleosynthesis and it's interesting we talked about stars and nucleosynthesis 10 00:00:37,402 --> 00:00:41,993 and the R process and the S process and supernovae as creating all the heavy 11 00:00:41,993 --> 00:00:45,632 elements. But we never discussed the production of 12 00:00:45,632 --> 00:00:48,924 Helium, of course, Helium is produced in stars. 13 00:00:48,924 --> 00:00:54,238 But we saw that not in a quantity that would significantly alter the sort of 14 00:00:54,238 --> 00:00:59,318 cosmic abundance of Helium. Where did the 25% of the universe that is 15 00:00:59,318 --> 00:01:03,593 Helium come from? And this becomes clear in a project 16 00:01:03,593 --> 00:01:08,311 undertaken by George Gamow and his student, Alpher, in 1948 and they 17 00:01:08,311 --> 00:01:13,601 actually, Gamow's agenda, the time stellar dynamics was not nearly as well 18 00:01:13,601 --> 00:01:19,067 understood as it is today, Gamow's agenda was to show that back in the hot, dense, 19 00:01:19,067 --> 00:01:24,509 early universe all of the elements were, in fact synthesized and that the current 20 00:01:24,509 --> 00:01:30,020 cosmic abundances could be explained by the Big Bang. So, what's the idea? If you 21 00:01:30,020 --> 00:01:34,981 go far enough in the past, there was a brief episode in the early history of the 22 00:01:34,981 --> 00:01:40,227 universe where temperatures were high and densities as high as in the interior of 23 00:01:40,227 --> 00:01:43,260 stars. So, there was fusion going on everywhere 24 00:01:43,260 --> 00:01:47,595 at every position, right here, what is the position that is 25 00:01:47,595 --> 00:01:53,649 right here, right now, a long time ago was a part of a very hot, dense plasma 26 00:01:53,649 --> 00:01:59,345 where fusion was going on. So, fusion was going on pervasively, and 27 00:01:59,345 --> 00:02:04,503 Gamow's idea was that this is where heavier elements than hydrogen were 28 00:02:04,503 --> 00:02:07,261 created. It turns out that, remember that the 29 00:02:07,261 --> 00:02:11,785 crucial step for synthesizing heavy elements was the triple alpha process. 30 00:02:11,785 --> 00:02:16,996 the triple alpha process worked in the context of a star that had long enough 31 00:02:16,996 --> 00:02:20,555 time to maintain a stellar core as high density for a while. 32 00:02:20,555 --> 00:02:25,585 only very rapid processes work in the context of Big Bang nucleosynthesis 33 00:02:25,585 --> 00:02:30,291 because very rapidly, the world cools and dilutes, and densities decrease, you 34 00:02:30,291 --> 00:02:35,129 don't have the stellar envelope holding things in, but it does correctly predict 35 00:02:35,129 --> 00:02:38,019 the Helium abundance, let's see how that works. 36 00:02:38,019 --> 00:02:43,642 So, here's the assumptions. We're going to assume, that reactions maintain 37 00:02:43,642 --> 00:02:48,917 thermal status of thermal equilibrium in the gas, this hot dense plasma, 38 00:02:48,917 --> 00:02:51,802 in the context of an expanding flat universe. 39 00:02:51,802 --> 00:02:56,722 This means that the reactions proceed rapidly enough that before the universe 40 00:02:56,722 --> 00:03:01,139 has diluted things away chemical abundances can adjust. And, of 41 00:03:01,139 --> 00:03:05,810 course, at some point, it stops and that is the, at that point, you sort of freeze 42 00:03:05,810 --> 00:03:09,535 in the situation that you have. So, let's see how that works. 43 00:03:09,535 --> 00:03:14,307 remember that at high temperature, we have relativistic particles and the 44 00:03:14,307 --> 00:03:19,297 number density of a relativistic particle is simply given by the Stefan-Boltzmann 45 00:03:19,297 --> 00:03:22,068 Law. The energy density of a relativistic gas 46 00:03:22,068 --> 00:03:26,622 is proportional to t^4, the energy, average energy of the particles 47 00:03:26,622 --> 00:03:31,304 proportional to t, so the number density of relativistic particles is proportional 48 00:03:31,304 --> 00:03:35,598 to kT^3, and in particular, is essentially independent of their masses. 49 00:03:35,598 --> 00:03:40,321 On the other hand, at the low energy, at low temperature we have non-relativistic 50 00:03:40,321 --> 00:03:42,813 particles. And if you imagine that there are 51 00:03:42,813 --> 00:03:45,932 processes that can create all kinds of particles 52 00:03:45,932 --> 00:03:51,750 then you can think of particles as energy states, as and just in the way that in a 53 00:03:51,750 --> 00:03:57,493 gas with temperature T, there can be a tail, remember, of particles, Helium 54 00:03:57,493 --> 00:04:03,290 particles, whose speeds are 10 times the average thermal speed but that's an 55 00:04:03,290 --> 00:04:08,469 exponential decaying tail. the similar process holds in creating 56 00:04:08,469 --> 00:04:13,624 particles of the, thermal equilibrium where there are processes that can create 57 00:04:13,624 --> 00:04:18,603 and destroy particles at temperatures below where kBT is less than mc^2 the 58 00:04:18,603 --> 00:04:23,181 number density of a particle decreases exponentially with the ratio of rest 59 00:04:23,181 --> 00:04:28,187 energy to the thermal energy, particles that are way massive than the pervase, 60 00:04:28,187 --> 00:04:32,787 more massive than the pervasive temperature are unlikely to be found and 61 00:04:32,787 --> 00:04:37,232 as this exponent approaches 0, you'll exactly go over to the relativistic mass 62 00:04:37,232 --> 00:04:40,732 indpendent density. So, whose radiation? Well, that depends 63 00:04:40,732 --> 00:04:44,629 on your temperature. I remind you of our list of particles. 64 00:04:44,629 --> 00:04:50,112 I've slightly increased it from back when you were talking about the sun, you see 65 00:04:50,112 --> 00:04:53,611 their charges. And based on their masses, I can tell you 66 00:04:53,611 --> 00:04:57,973 that protons, for example, become relativistic of temperatures of about 67 00:04:57,973 --> 00:05:01,045 10^13 K. And this g is that geometric factor, the 68 00:05:01,045 --> 00:05:05,937 number of degenerate states that a particle has that relates how many of 69 00:05:05,937 --> 00:05:08,820 these there are to how many photons there are. 70 00:05:08,820 --> 00:05:11,804 So, that's an extra factor of our [UNKNOWN] density. 71 00:05:11,804 --> 00:05:14,826 protons become relativistic at 10^13 Kelvin. 72 00:05:14,826 --> 00:05:18,150 What about neutrons? Well, neutrons are a little bit more 73 00:05:18,150 --> 00:05:22,444 massive than protons so they become relativistic at a temperature that is 74 00:05:22,444 --> 00:05:27,557 just a little bit higher 10^13, but the main important difference is that the 75 00:05:27,557 --> 00:05:33,402 temperature difference for neutrons to become relativistic is about 1.5*10^10 K. 76 00:05:33,402 --> 00:05:39,112 Electrons, being much lighter become relativistic at about 6 billion Kelvin. 77 00:05:39,112 --> 00:05:42,057 neutrinos, as far as we know, are massless. 78 00:05:42,057 --> 00:05:45,617 They can become relativistic at any temperature. 79 00:05:45,617 --> 00:05:51,232 Certainly a photon, which is exactly massless is relativistic at all, 80 00:05:51,232 --> 00:05:55,352 temperatures isn't always moves at the speed of light. 81 00:05:55,352 --> 00:06:01,002 muons, intermediate mass become relativistic at about a trillion K. 82 00:06:01,002 --> 00:06:06,982 And another kind of particle called the pion, this is not the right number and 83 00:06:06,982 --> 00:06:13,645 the mass of a pion is 140 some, 2 maybe MeV and so they become relativistic at 84 00:06:13,645 --> 00:06:17,618 about 1.6 trillion degrees, there's 3 different kinds of them with three 85 00:06:17,618 --> 00:06:20,951 different charges and this is a relic from an old table. 86 00:06:20,951 --> 00:06:25,486 okay, so there's a collection of particles and as temperatures increase 87 00:06:25,486 --> 00:06:29,192 moving into the past, more and more of them are relativistic. 88 00:06:29,192 --> 00:06:33,838 So, what has this got to tell us? conversely as temperatures cool, less and 89 00:06:33,838 --> 00:06:38,099 less of them are relativistic. So, let's start at the beginning with a 90 00:06:38,099 --> 00:06:41,858 very hot universe with a temperature above a trillion Kelvin. 91 00:06:41,858 --> 00:06:46,580 neutrons and protons are marginally non-relativistic but of all the species 92 00:06:46,580 --> 00:06:51,059 that are relativistic, then you have thermal equilibrium. And in thermal 93 00:06:51,059 --> 00:06:54,402 equilibrium, as we'll see, the processes of Physics do not 94 00:06:54,402 --> 00:06:58,442 distinguish particles from antiparticles so there is as many antielectrons as 95 00:06:58,442 --> 00:07:01,602 there are electrons. There is as many antiprotons as protons, 96 00:07:01,602 --> 00:07:04,567 there are almost as many. So, there are large quantites of 97 00:07:04,567 --> 00:07:08,607 antiprotons and protons, antineutrinos and neutrinos, antimuons and muons, and 98 00:07:08,607 --> 00:07:11,377 so on. the ratio between the number density of 99 00:07:11,377 --> 00:07:16,337 neutrons and protons is given by the ratio of those two exponentials which is 100 00:07:16,337 --> 00:07:21,287 proportional to the difference of their masses in units of kT and since the 101 00:07:21,287 --> 00:07:26,327 difference in their masses is small compared to the temperature even though 102 00:07:26,327 --> 00:07:31,654 they're not relativistic, there's about the same number of neutrons as protons. 103 00:07:31,654 --> 00:07:34,714 Now, as the universe cools by about a factor of 10, 104 00:07:34,714 --> 00:07:39,687 by the way, these temperatures obtained for the first ten thousandths of a second 105 00:07:39,687 --> 00:07:44,641 after the Planck time, so we're deep into the radiation dominated era and all of 106 00:07:44,641 --> 00:07:48,899 the exciting events occur very early in the history of the univesre. 107 00:07:48,899 --> 00:07:53,552 by that time temperatures have decreased by about 10^11 Kelvin. 108 00:07:53,552 --> 00:07:57,796 muons stop being relativistic. When muons slow down, these muons and 109 00:07:57,796 --> 00:08:00,570 antimuons find each other, they annihilate. 110 00:08:00,570 --> 00:08:05,269 most of the muons are gone, only a small remnant of actual muons survive. 111 00:08:05,269 --> 00:08:10,273 The excess muons over antimuons, we'll talk about that later, and the muons are 112 00:08:10,273 --> 00:08:13,989 gone by this time. If you plug into this expression there's 113 00:08:13,989 --> 00:08:18,208 still equilibrium, the number of neutrons, ratio of neutron number to 114 00:08:18,208 --> 00:08:23,146 proton number is about 0.86 and note [COUGH] that neutrons, unlike protons, 115 00:08:23,146 --> 00:08:24,751 are unstable. Of course, 116 00:08:24,751 --> 00:08:27,616 they decay. But they decay in 15 minutes. 117 00:08:27,616 --> 00:08:31,122 Neutron decay is not playing a significant role yet. 118 00:08:31,122 --> 00:08:35,133 It will later. as the temperature cools further by the 119 00:08:35,133 --> 00:08:41,573 time we get to 30 billion K at time about a tenth of a second after the Big Bang 120 00:08:41,573 --> 00:08:47,697 neutrinos, because of the slow rates of the weak interactions essentially 121 00:08:47,697 --> 00:08:53,821 decouple at this point neutrons or neutron to proton ratio has decreased to 122 00:08:53,821 --> 00:08:58,594 about 0.6. And by the time you get to 5 billion Kelvin at a few tens of seconds 123 00:08:58,594 --> 00:09:03,006 electrons have become, are beginning to become non-relativistic, electrons and 124 00:09:03,006 --> 00:09:05,854 positrons annihilate, producing a lot of photons. 125 00:09:05,854 --> 00:09:09,179 Notice that the, the neutrinos are, are already decoupled. 126 00:09:09,179 --> 00:09:13,067 So, at the time that the neutrinos decoupled, of course, neutrinos and 127 00:09:13,067 --> 00:09:18,012 photons were all strongly interacting. There were two gases that could exchange 128 00:09:18,012 --> 00:09:22,682 energy, they had the same temperature. So, do we expect a gas of primordial 129 00:09:22,682 --> 00:09:27,512 neutrinos, just as there are cosmic microwave backgrounds, sort of, except 130 00:09:27,512 --> 00:09:33,589 that when all these electrons annihilated electron and positron produce two photons 131 00:09:33,589 --> 00:09:39,126 with energy 511 KeV each. And so this produces more photons heating 132 00:09:39,126 --> 00:09:45,756 the photon gas injecting energy into the photon gas that is then rethermalized. 133 00:09:45,756 --> 00:09:51,702 And for that reason, the photons at that point are harder than neutrinos. 134 00:09:51,702 --> 00:09:57,421 From that moment on after recombination, photons evolve the same way as neutrinos, 135 00:09:57,421 --> 00:10:01,880 they are temporarily, they remain blackbody and their temperature decreases 136 00:10:01,880 --> 00:10:05,975 with the scale factor. So, the ratio between photon temperatures 137 00:10:05,975 --> 00:10:10,672 and neutrino temperatures was in, sort of implanted at the time of electron 138 00:10:10,672 --> 00:10:14,144 annihilation. And the neutrinos are colder than the 139 00:10:14,144 --> 00:10:18,656 photons by the factor of 1.4, so there's less energy in neutrinos than there is in 140 00:10:18,656 --> 00:10:22,982 photons, but there is definitely an ambient cosmic neutrino radiation flying 141 00:10:22,982 --> 00:10:25,281 around. But that's not what we're about. 142 00:10:25,281 --> 00:10:29,474 We're talking about the neutrinos, about the neutrons and the protons because 143 00:10:29,474 --> 00:10:34,525 that's what it takes to make Helium. Notice that unlike in the present 144 00:10:34,525 --> 00:10:39,252 universe, in the present universe, you mostly find protons, neutrons only exist 145 00:10:39,252 --> 00:10:42,037 in nuclei. That's because they have billions of 146 00:10:42,037 --> 00:10:44,591 years to decay. Free neutrons do not exist. 147 00:10:44,591 --> 00:10:47,682 At these short times, neutrons have not decayed yet. 148 00:10:47,682 --> 00:10:52,636 Now, back when the universe was hot and dense the protons and neutrons are in 149 00:10:52,636 --> 00:10:56,698 chemical equilibrium, there are these rapid reactions that can 150 00:10:56,698 --> 00:11:01,495 convert neutrons to protons and protons to neutrons, in the presence of this sea 151 00:11:01,495 --> 00:11:05,755 of electrons and neutrinos, as the temperatures cool and the neutrinos 152 00:11:05,755 --> 00:11:08,265 decouple. And soon thereafter, most of the 153 00:11:08,265 --> 00:11:15,481 electrons and the positrons disappear. this reaction slow down by that time the 154 00:11:15,481 --> 00:11:23,264 neutron to proton ratio is decreased to about 0.22 because at this temperature, 155 00:11:23,264 --> 00:11:31,850 the mass difference is significant, it's either minus 1.5. Now, notice that once 156 00:11:31,850 --> 00:11:36,386 this ratio is achieved and temperatures have decreased, 157 00:11:36,386 --> 00:11:41,372 this ratio is frozen in essentially because reactions converting protons to 158 00:11:41,372 --> 00:11:45,034 neutrons and back, and vice-versa, no longer take place. 159 00:11:45,034 --> 00:11:48,934 So, from this moment on, these are the neutrons that you have. 160 00:11:48,934 --> 00:11:53,672 Now so now, you have a gas of neutrons and protons and, of course, over time, 161 00:11:53,672 --> 00:11:57,232 the neutrons decay so you have less and less neutrons. 162 00:11:57,232 --> 00:12:01,791 However, the universe is cooling and expanding and cooling, and when 163 00:12:01,791 --> 00:12:06,790 temperatures cool down to about a billion Kelvin, that is a time of about 180 164 00:12:06,790 --> 00:12:10,188 seconds after the Big Bang, Deuterium is stable. 165 00:12:10,188 --> 00:12:15,005 So, if a proton and a neutron happen to be moving slowly enough next to each 166 00:12:15,005 --> 00:12:19,628 other and bind to form Deuterium, Deuterium will not be blown apart, 167 00:12:19,628 --> 00:12:24,536 photodisintegrated, by high energy photons once the energy of the photons is 168 00:12:24,536 --> 00:12:29,242 less than a billion kelvin. So until that time there was no Deuterium 169 00:12:29,242 --> 00:12:34,077 because if Deuterium, formed it would of been blown apart by a photon after 180 170 00:12:34,077 --> 00:12:37,032 seconds after the Big Bang, Deuterium can form. 171 00:12:37,032 --> 00:12:42,382 Now, at this point essentially all of the neutrons that are left form Deuterium. 172 00:12:42,382 --> 00:12:47,712 How many neutrons are left? Well, they had a fraction of about 0.223 of neutrons 173 00:12:47,712 --> 00:12:53,500 to protons, but 180 seconds have gone by. The half-life of a neutron these are free 174 00:12:53,500 --> 00:12:57,983 neutrons, is about 600 seconds. you plug that into our half-life 175 00:12:57,983 --> 00:13:03,442 radioactive decay formula, remembering that neutrons decay to protons so it's 176 00:13:03,442 --> 00:13:08,464 parent to daughter ratio the number of neutrons has decreased, protons 177 00:13:08,464 --> 00:13:14,147 increased, The ratio has approximately halved, by this time, only about 12% of 178 00:13:14,147 --> 00:13:19,688 the baryons in the universe are neutrons. And now, once Deuterium is stable a 179 00:13:19,688 --> 00:13:24,391 neutron inside the Deuteron is stable, neutrons stop decaying. 180 00:13:24,391 --> 00:13:29,611 Essentially, all of the remaining neutrons are bound up in Deuterium and 181 00:13:29,611 --> 00:13:35,706 very rapidly thereafter, they formed a very stable alpha particle nucleus. So, 182 00:13:35,706 --> 00:13:40,428 essentially, all of the neutrons that survive produce Helium. 183 00:13:40,428 --> 00:13:46,074 And so, we get left with a Helium nuclei and three protons and no more neutrons. 184 00:13:46,074 --> 00:13:53,221 So, what does this predict about how many Helium nuclei you will have formed? Well, 185 00:13:53,221 --> 00:13:58,143 you can figure it out. how many of the nuclei that we have left 186 00:13:58,143 --> 00:14:03,610 are Helium nuclei? Well, each Helium nucleus requires 2 protons, 2, and 2 187 00:14:03,610 --> 00:14:09,130 neutrons, since we had this many neutrons, this was our neutron to proton 188 00:14:09,130 --> 00:14:14,753 ratio, divide that by 2, that's sort of a count of how many neutrons how many 189 00:14:14,753 --> 00:14:18,972 Helium nuclei were created. How many particles 190 00:14:18,972 --> 00:14:25,586 what is the total number of particles? Well, we had a sort of the total number 191 00:14:25,586 --> 00:14:32,932 of neutrons plus protons. Add that up to 1 but then each new, each 192 00:14:32,932 --> 00:14:39,452 formation of a Helium nucleus took away 2 protons and took away 2 neutrons. So this 193 00:14:39,452 --> 00:14:47,648 many this many Helium nuclei took away four particles, replaced them by one so 194 00:14:47,648 --> 00:14:52,137 each Helium nucleus reduced the number by three. 195 00:14:52,137 --> 00:15:00,109 Plug in these numbers, you find that 7.5% of all the particles that are left in 196 00:15:00,109 --> 00:15:05,554 your all the baryons that are left are Helium nuclei and, of course, the others 197 00:15:05,554 --> 00:15:08,619 are protons. And any free neutrons that were left 198 00:15:08,619 --> 00:15:13,300 around that did not get stopped in, will rapidly within, you know, a few minutes, 199 00:15:13,300 --> 00:15:17,017 decay and so you'll, you'll end up with protons and alpha 200 00:15:17,017 --> 00:15:22,132 particles, that's all you'll end up with. So this is the fraction of the universe 201 00:15:22,132 --> 00:15:26,917 that you predict by this very rough calculation, will be Helium and in terms 202 00:15:26,917 --> 00:15:31,592 of mass, since the mass of a Helium nucleus is 4 times the mass of a proton, 203 00:15:31,592 --> 00:15:35,352 the mass fraction of Helium that you predict is about 30%. 204 00:15:35,352 --> 00:15:38,386 this is not bad. Remember, what we observe is about a 205 00:15:38,386 --> 00:15:41,093 quarter of the mass of the universe is in Helium. 206 00:15:41,093 --> 00:15:45,777 This very rough calculation produces an result that is very close to correct, 207 00:15:45,777 --> 00:15:48,535 a more refined calculation produces agreement. 208 00:15:48,535 --> 00:15:52,854 Notice that since essentially, all I needed to know was the ratio of neutrons 209 00:15:52,854 --> 00:15:55,536 to protons, it's very insensitive to details. 210 00:15:55,536 --> 00:16:00,693 the rate at which the universe cools, it's a radiation dominated universe, that 211 00:16:00,693 --> 00:16:04,875 has to do with the density of photons in the universe which I know because I 212 00:16:04,875 --> 00:16:07,840 measure the cosmic microwave background radiation. 213 00:16:07,840 --> 00:16:11,637 I know the energy density in the thermal microwave background. 214 00:16:11,637 --> 00:16:15,744 Today, I can extrapolate that by energy conservation back to those times. 215 00:16:15,744 --> 00:16:19,352 There is very little ambiguity. There's no free paramiters. 216 00:16:19,352 --> 00:16:24,560 And then, that get, that sets the time rate for all of these reactions to occur 217 00:16:24,560 --> 00:16:30,523 and basically nothing depends on any of the details the fraction of the universe, 218 00:16:30,523 --> 00:16:35,578 the protons and the neutrons that are converted to Helium atoms is a very 219 00:16:35,578 --> 00:16:40,020 robust prediction. Okay. So, we can understand where Helium 220 00:16:40,020 --> 00:16:43,361 came from. But about other nuclei, remember, gamma 221 00:16:43,361 --> 00:16:47,284 was trying to produce all nucleons, all nuclear, nuclear species. 222 00:16:47,284 --> 00:16:53,420 It turns out that fusion to heavier nuclei than Helium is very inefficient, 223 00:16:53,420 --> 00:17:00,001 but you form some small fraction of trace amounts of lithium and excitingly a 224 00:17:00,001 --> 00:17:05,450 little bit of Helium 3 and excitingly a fraction of, a small fraction of 225 00:17:05,450 --> 00:17:09,549 Deuterium. So, some of the deuterons did not fuse to 226 00:17:09,549 --> 00:17:15,759 form Helium and how many of them did not fuse to form Helium depends on the speed 227 00:17:15,759 --> 00:17:22,122 in which the universe expands driven by, remember, the density of the photon gas, 228 00:17:22,122 --> 00:17:28,143 relative to the density of nucleons because the denser nucleons are, the more 229 00:17:28,143 --> 00:17:33,552 rapid nuclear reactions are. So the abundance of Deuterium is very 230 00:17:33,552 --> 00:17:39,890 sensitive to this ratio of the density of baryons to the density of radiation and 231 00:17:39,890 --> 00:17:46,406 since today, density predicts the density then you can put constraints on the 232 00:17:46,406 --> 00:17:53,192 baryon density relative to the density of radiation, which remember, is known 233 00:17:53,192 --> 00:17:57,914 because this is basically sigma times 2.7k^4/2c. 234 00:17:57,914 --> 00:18:01,908 I know this. Well, this is rho radiation at current 235 00:18:01,908 --> 00:18:06,501 time. The background radiation gives me omegaR, 236 00:18:06,501 --> 00:18:10,366 precisely. So, this gives me great, strong 237 00:18:10,366 --> 00:18:16,341 constraints on the baryon density. This, in the sense, tells us two things. 238 00:18:16,341 --> 00:18:21,865 one is it tells us that not more than 5% of the total energy of the universe or 239 00:18:21,865 --> 00:18:27,608 the critical density could possibly be baryons, else we would have been left 240 00:18:27,608 --> 00:18:32,294 with lots more Deuterium. And I should point out that there are 241 00:18:32,294 --> 00:18:39,204 very few processes after the Big Bang that are likely to form Deuterium without 242 00:18:39,204 --> 00:18:45,166 producing alpha this is a a process of Nuclear Physics. 243 00:18:45,166 --> 00:18:52,926 and furthermore, it tells us that so, so that if we find that the density of dust 244 00:18:52,926 --> 00:18:58,792 of matter, non-relativistic matter in the universe, is larger than that 5%, then 245 00:18:58,792 --> 00:19:03,507 the remaining amount must be non-baryonic, and therefore, this is the 246 00:19:03,507 --> 00:19:07,427 25% of the universe, that we think is composed of dark matter. 247 00:19:07,427 --> 00:19:12,897 This is one of the strongest constraints. you can, of course, do some more refined 248 00:19:12,897 --> 00:19:18,083 calculations that take into account both the concentration of Helium and of 249 00:19:18,083 --> 00:19:22,717 various isotopes and as I said, the trace amount of Lithium that was produced and 250 00:19:22,717 --> 00:19:25,138 so, this gives us a constraint on Cosmology. 251 00:19:25,138 --> 00:19:28,879 Moreover, if you tweak your model of particle Physics by all kinds of 252 00:19:28,879 --> 00:19:33,624 additions to the standard model trying to understand as we will see theories beyond 253 00:19:33,624 --> 00:19:36,774 the standard model, they might make small modifications to 254 00:19:36,774 --> 00:19:41,035 the rates of these nuclear reactions. things are extremely sensitive to the 255 00:19:41,035 --> 00:19:44,558 rates of nuclear reaction. For example, you can do a rather straight 256 00:19:44,558 --> 00:19:48,363 forward calculation that shows that if there were more than three, remember, 257 00:19:48,363 --> 00:19:52,525 there were three species of light neutrinos the muon neutrino, the electron 258 00:19:52,525 --> 00:19:57,599 neutrino, and the tau neutrino. more than three species of light neutrino 259 00:19:57,599 --> 00:20:03,375 would lead to unacceptable to Deuterium concentrations that are incompatible with 260 00:20:03,375 --> 00:20:08,053 the observation and so, in that sense, we know there cannot be a fourth as yet 261 00:20:08,053 --> 00:20:13,708 undetected neutrino species because it would ruin Big Bang nucleosynthesis, a 262 00:20:13,708 --> 00:20:18,653 very sensitive test of our understanding both of Cosmology and of particle Physics 263 00:20:18,653 --> 00:20:21,729 and one of the great successes of Big Bang Cosmology