1 00:00:00,012 --> 00:00:05,334 So, we have our model. It's called Lambda Cold Dark Matter 2 00:00:05,334 --> 00:00:12,962 Cosmology because it assumes that the missing energy in the universe beyond the 3 00:00:12,962 --> 00:00:20,242 5% that is us, is dark matter, which is cold because we want it to clump to form 4 00:00:20,242 --> 00:00:24,919 the dark matter outline of galaxies. We said that we are not talking about 5 00:00:24,919 --> 00:00:29,272 relativistic particles, but about particles that are very massive when we 6 00:00:29,272 --> 00:00:34,642 talked talked about dark matter and lambda for cosmological constant and this 7 00:00:34,642 --> 00:00:39,342 is LCDM standard cosmology. And the problem is solved, right? Not 8 00:00:39,342 --> 00:00:43,272 everything. So, there are some issues in the study of 9 00:00:43,272 --> 00:00:50,102 cosmology and in another one of the fun parts of this field the study of the 10 00:00:50,102 --> 00:00:56,008 universe at its very largest reduces the study of the universe at very small sizes 11 00:00:56,008 --> 00:01:01,489 because you need to study what is very far, what is very far you're seeing into 12 00:01:01,489 --> 00:01:05,107 the deep past. In the deep past, it was actually very 13 00:01:05,107 --> 00:01:08,434 dense. Now I want to make a point about this 14 00:01:08,434 --> 00:01:12,892 past and very dense. The universe in the past was very dense. 15 00:01:12,892 --> 00:01:18,032 The universe is flat, we have every reason to assume that it is infinite. 16 00:01:18,032 --> 00:01:24,037 one often hears that in the past, moments after the Big Bang, the entire universe 17 00:01:24,037 --> 00:01:27,339 was a tiny, dense marble the size of a nucleus. 18 00:01:27,339 --> 00:01:32,716 This is correct, but very misleading. Yes, the entire visible chunk of the 19 00:01:32,716 --> 00:01:37,588 universe, the entire 46 million billion light years radius sphere that we see 20 00:01:37,588 --> 00:01:41,415 today was, in fact, condensed to something the size of a nucleus at some 21 00:01:41,415 --> 00:01:43,739 point. However, that was not the end of the 22 00:01:43,739 --> 00:01:47,738 universe nor it, is there any reason to assume that that's the end of the 23 00:01:47,738 --> 00:01:52,017 universe, anymore than there would have been a reason, 8 billion years ago for 24 00:01:52,017 --> 00:01:55,922 some astronomer to conclude that the universe is only half that size. 25 00:01:55,922 --> 00:02:01,190 Since then, our particle horizon has doubled and we see more of much the same 26 00:02:01,190 --> 00:02:04,481 universe. And there's every reason to assume that 27 00:02:04,481 --> 00:02:09,213 when see out to 62 billion light years, we will see about more of the same 28 00:02:09,213 --> 00:02:12,433 universe. And what's more, this is also true of 29 00:02:12,433 --> 00:02:17,651 someone who lives 40 billion light years that way and they see an additional 40 30 00:02:17,651 --> 00:02:21,606 billion light years that way. So, we have every reason to assume that 31 00:02:21,606 --> 00:02:25,740 the universe is homogeneous and isotropic even beyond what we've directly observed 32 00:02:25,740 --> 00:02:29,413 because otherwise again, we're putting ourselves in some kind of crazy 33 00:02:29,413 --> 00:02:32,230 anthropocentric. We're in the middle of the homogeneous 34 00:02:32,230 --> 00:02:34,960 patch and there's an edge just beyond where we can see. 35 00:02:34,960 --> 00:02:37,852 That's ridiculous. So, the universe was never the size of a 36 00:02:37,852 --> 00:02:40,208 marble. The universe was very dense but if it's 37 00:02:40,208 --> 00:02:43,402 infinite today, it was infinite then, it was just much denser. 38 00:02:43,402 --> 00:02:47,229 Off the soap box. how does the physics of very small come 39 00:02:47,229 --> 00:02:53,752 in? Well, of course, at early times and very high densities, by which time we 40 00:02:53,752 --> 00:03:00,561 measure the density not by the redshift and not by the scale factor but by the 41 00:03:00,561 --> 00:03:07,545 energy, effective energy KBT of the radiation dominated universe. So, when 42 00:03:07,545 --> 00:03:14,406 this energy is above 10^19 GeV, a huge energy, this is in the first 5*10^-44 43 00:03:14,406 --> 00:03:20,109 seconds after the Big Bang quantum gravitational effects are important. 44 00:03:20,109 --> 00:03:22,890 So, this is the vicinity of the singularity. 45 00:03:22,890 --> 00:03:28,143 Remember, that our expanding universe, if you follow it back, leads to an actual 46 00:03:28,143 --> 00:03:33,108 singularity in the relativistic GR equations as actual singularity in the 47 00:03:33,108 --> 00:03:38,582 sense that the curvature was infinite and everywhere in the distant past in this 48 00:03:38,582 --> 00:03:43,157 infinite universe. at the Big Bang, curvature is infinite Gr 49 00:03:43,157 --> 00:03:45,857 breaks down. A little bit after that, our 50 00:03:45,857 --> 00:03:51,032 understanding of physics breaks down because so, maybe quantum gravity will 51 00:03:51,032 --> 00:03:56,572 fix the singularity. even at energies below this Planck energy 52 00:03:56,572 --> 00:04:04,192 of 10^19 GeV or times after 5810^-44. by the time you reach order, 10 orders of 53 00:04:04,192 --> 00:04:12,602 magnitude higher, 10^-34 seconds KBT has dropped down to 10^15 GeV at that energy. 54 00:04:12,602 --> 00:04:17,955 from that energy down, we sort of have a model of physics that works, the standard 55 00:04:17,955 --> 00:04:22,292 model determines the physics. We have not made measurements up to that 56 00:04:22,292 --> 00:04:27,788 energy, we have we have made measurements up to a 1,000 GeV but we think that we 57 00:04:27,788 --> 00:04:33,041 have reason to understand that he next corrections to Physics are suggested at a 58 00:04:33,041 --> 00:04:37,526 scale of about 10 to the 15 GeV. Above 10^15 GeV, we think We we have 59 00:04:37,526 --> 00:04:42,198 reason, theoretical biases to suggest that, in fact, the electroweak and the 60 00:04:42,198 --> 00:04:45,923 strong interaction are part of one grand unified theory. 61 00:04:45,923 --> 00:04:50,827 There are various versions of the Grand Unified Theory, they share some common 62 00:04:50,827 --> 00:04:56,339 properties but they would be necessary if you wanted to describe that part of the 63 00:04:56,339 --> 00:05:02,057 history of the universe prior to 10^-34 seconds, and after, quantum gravity 64 00:05:02,057 --> 00:05:08,799 corrections became unimportant. one aspect of this, is that if you tried 65 00:05:08,799 --> 00:05:14,986 to make a prediction for the value of the cosmological constant, of the vacuum 66 00:05:14,986 --> 00:05:20,407 energy, from these theories, well, you can build theories in which the 67 00:05:20,407 --> 00:05:25,927 cosmological constant is 0 if, but if you don't build theories in which it's 68 00:05:25,927 --> 00:05:31,152 exactly 0, then the typical value for lambda that you find is off by about 69 00:05:31,152 --> 00:05:34,437 10^60. This is one of the largest glaring 70 00:05:34,437 --> 00:05:37,732 misunderstood ununderstood aspects of physics. 71 00:05:37,732 --> 00:05:42,353 so this is one problem to which I will not propose a solution today. 72 00:05:42,353 --> 00:05:47,840 how to make a cosmological constant that is not zero and is not ridiculously 73 00:05:47,840 --> 00:05:51,108 large. Open problem in particle physics and 74 00:05:51,108 --> 00:05:56,618 again, with cosmological applications but it's in the nature of Physics at very 75 00:05:56,618 --> 00:06:02,532 small scales to determine this. what are the problems beyond at energies 76 00:06:02,532 --> 00:06:07,157 lower than that? Well, there are three famous problems with our scenario. 77 00:06:07,157 --> 00:06:11,257 One is that the cosmic microwave background is so isotropic. 78 00:06:11,257 --> 00:06:16,382 Well, I thought that was a great thing. It showed us that the universe is really 79 00:06:16,382 --> 00:06:22,415 isotropic, yes, but how did it get so isotropic? So we computed that 1 degree 80 00:06:22,415 --> 00:06:28,644 was the distance a sound wave could have traveled in the 380 degrees thousand 81 00:06:28,644 --> 00:06:33,568 years since the Big Bang. light travels at a square root of 3 82 00:06:33,568 --> 00:06:39,239 faster, so square root of 3 degrees is the size of a region in the sky that 83 00:06:39,239 --> 00:06:42,238 light could have traveled since the Big Bang. 84 00:06:42,238 --> 00:06:47,506 So, regions in the sky separated by more than the square root of 3 degrees had not 85 00:06:47,506 --> 00:06:52,584 heard from each other by the time of recombination and by the this, the time 86 00:06:52,584 --> 00:06:57,329 that the cosmic microwave background radiation that we see was emitted as 87 00:06:57,329 --> 00:07:00,551 photons at 3,000 Kelvin. So, how could the temperature be so 88 00:07:00,551 --> 00:07:04,920 precisely equal to within 1 part of 10^-5 in regions that had not talked to each 89 00:07:04,920 --> 00:07:08,871 other? You'd expect fluctuations to cause one region to be hotter and another to be 90 00:07:08,871 --> 00:07:12,373 colder and then heat to flow from the hot region to the cold region until 91 00:07:12,373 --> 00:07:15,142 equilibrium. Yeah, but you can't establish equilibrium 92 00:07:15,142 --> 00:07:20,057 if you haven't heard from each other yet. So, the very uniformity of the cosmic 93 00:07:20,057 --> 00:07:26,137 microwave background is a puzzle, we have no mechanism. I mean, you can posit 94 00:07:26,137 --> 00:07:32,067 initial conditions that very precisely homogeneous but that's unnatural, one 95 00:07:32,067 --> 00:07:35,685 problem. Second problem is the flatness problem. 96 00:07:35,685 --> 00:07:42,021 We measure that today's density is very close to the critical density, the 97 00:07:42,021 --> 00:07:47,064 universe is almost exactly flat. Well, this tells you that in prior 98 00:07:47,064 --> 00:07:52,411 epochs, the universe was even more flat. in particular, in our dust universe 99 00:07:53,442 --> 00:08:00,212 where, remember, universe so, ignore the cosmological constant just so we can do 100 00:08:00,212 --> 00:08:04,800 calculations. Imagine that we have a critical universe 101 00:08:04,800 --> 00:08:10,987 where the only type of matter is dust, in other words rho of t is rho 0 times 102 00:08:10,987 --> 00:08:18,806 a(t)^-3, that's what being dust buys me. And so, we have this relation that's it 103 00:08:18,806 --> 00:08:23,696 well, it defined domain omega as 8 pi G rho over 3H^2. 104 00:08:23,696 --> 00:08:30,101 So, at any time, H^2 omega is 8 opi G rho over 3 and in particular, this holds at 105 00:08:30,101 --> 00:08:37,075 the present time with omega 0 and H 0. The other relation was that omega-1 was 106 00:08:37,075 --> 00:08:43,029 this over H^2, a^2. So, I put the H^2 over here so H^2 times 107 00:08:43,029 --> 00:08:52,713 omega-1 is kR0c^2/a^2. And now this is true at all times, so in 108 00:08:52,713 --> 00:09:03,623 particular, I can write that H^2 omega at any time is the same as 8 pi G rho of t, 109 00:09:03,623 --> 00:09:12,030 and this is related to H0^2 omegas 0 squared by the factor of a^-3. 110 00:09:13,527 --> 00:09:26,112 And likewise, I can write that H^2 times omega-1 is H0^2 times omega0-1 except 111 00:09:26,112 --> 00:09:31,755 times a^-2. So, I have here two equations, if I know 112 00:09:31,755 --> 00:09:38,072 H0 and omega 0, I can figure H and omega. It's a little bit of Algebra, it's not 113 00:09:38,072 --> 00:09:43,779 too bad, and what you find for omega is this beautiful equation over here, 114 00:09:43,779 --> 00:09:49,822 omega-1, at any prior time, at any time in the evolution of a dust universe is 115 00:09:49,822 --> 00:09:56,185 related to omega0-1, by this expression. But, so what does that tell me? That 116 00:09:56,185 --> 00:10:02,414 tells me that if you go back to very small a in the dim past, then this term 117 00:10:02,414 --> 00:10:06,787 is essential small. This is omega 0, and you find that 118 00:10:06,787 --> 00:10:11,162 omega-1 is about a over omega 0, omega0-1. 119 00:10:12,338 --> 00:10:22,863 So omega-1 is much smaller than omega0-1 in the limit when a becomes very small. 120 00:10:22,863 --> 00:10:29,394 So, if we measure today, omega 0 approximately one to, within some 121 00:10:29,394 --> 00:10:37,766 accuracy, say, 1 part in 100 then at early times, when a was 10^-18, omega-1 122 00:10:37,766 --> 00:10:44,165 had to be 10^-18 more precisely 1. So again, posit initial conditions where 123 00:10:44,165 --> 00:10:48,044 omega, if omega is ever exactly 1, then, of course, it stays 1. 124 00:10:48,044 --> 00:10:52,441 So, one possibility is to find a mechanism that makes omega exactly 1. 125 00:10:52,441 --> 00:10:57,502 Or posit initial conditions that omega was close to 1 to within 180 orders of 126 00:10:57,502 --> 00:11:01,067 magnitude, or find a mechanism that makes that natural. 127 00:11:01,067 --> 00:11:05,827 So, these are aesthetic problems. there's a third problem associated to 128 00:11:05,827 --> 00:11:10,892 these GUT extensions of the standard model, they predict that as the universe 129 00:11:10,892 --> 00:11:17,147 cools from the GUT scale of 10^15 GeV and below there will be relics left over, 130 00:11:17,147 --> 00:11:23,337 magnetic monopoles that are stable and cannot decay unless they annihilate with 131 00:11:23,337 --> 00:11:29,272 magnetic anti-monopoles, and for, depending on the extension, various other 132 00:11:29,272 --> 00:11:32,762 relic particles. And magnetic monopole should be 133 00:11:32,762 --> 00:11:37,077 detectable, there have been ongoing searches and we find none, you could 134 00:11:37,077 --> 00:11:40,367 predict the density and we should have seen them by now. 135 00:11:40,367 --> 00:11:44,902 So, where are the magnetic monopoles? these three problems were addressed by 136 00:11:44,902 --> 00:11:47,532 something we'll talk about in the next clip. 137 00:11:47,532 --> 00:11:52,442 there is the first problem of the vanishing of the cosmological constant or 138 00:11:52,442 --> 00:11:57,382 the smallest of the cosmological constant is being addressed by theories of quantum 139 00:11:57,382 --> 00:12:01,949 gravity about which we'll say little. there is fifth problem that 140 00:12:01,949 --> 00:12:06,366 matter-antimatter asymmetry, the laws of Physics are almost but not quite 141 00:12:06,366 --> 00:12:10,155 symmetric under the exchange of particles with antiparticles. 142 00:12:10,155 --> 00:12:15,138 If they were precisely symmetric, then you would predict that the thermo bath 143 00:12:15,138 --> 00:12:19,112 the hot, dense, earlier universe would produce, in equilibrium, as many 144 00:12:19,112 --> 00:12:22,952 particles as antiparticles, as many antiprotons as protons, as many 145 00:12:22,952 --> 00:12:27,296 antineutrons as neutrons, and so on. In fact, you might get a small imbalance 146 00:12:27,296 --> 00:12:31,363 but it's important that you get an imbalance, because if you produced equal 147 00:12:31,363 --> 00:12:35,601 numbers of muons and antimuons, then when they became non-relativistic, all the 148 00:12:35,601 --> 00:12:39,265 muons would annihilate with all the antimuons and you'd have nothing left. 149 00:12:39,265 --> 00:12:42,954 The reason we have something left is because, for some reason, more muons were 150 00:12:42,954 --> 00:12:46,169 produced than antimuons. Now, this could be a fluctuation but then 151 00:12:46,169 --> 00:12:49,830 you'd expect that if, that, that, by and large, maybe you'd have some regions of 152 00:12:49,830 --> 00:12:53,575 the universe that are made of matter where matter predominates other regions 153 00:12:53,575 --> 00:12:56,562 where antimatter predominates. But it's not true. 154 00:12:56,562 --> 00:13:01,335 cosmic rays that arrive from large distance [UNKNOWN] in the universe show 155 00:13:01,335 --> 00:13:05,778 us that our universe is almost exclusively made, all the galaxies and 156 00:13:05,778 --> 00:13:08,985 the stars are almost exclusively made of protons. 157 00:13:08,985 --> 00:13:14,120 There is not a star out there made up of antiprotons although in principle such a 158 00:13:14,120 --> 00:13:17,621 thing could exist. Antiprotons could bind antielectrons and 159 00:13:17,621 --> 00:13:20,253 produce atoms where everything is backwards, 160 00:13:20,253 --> 00:13:23,728 but that does not happen. In our universe, there is this large 161 00:13:23,728 --> 00:13:26,685 asymmetry. all the antimatter annihilated early and 162 00:13:26,685 --> 00:13:30,037 what we're left with is a universe with protons and electrons and neutrons and no 163 00:13:30,037 --> 00:13:33,210 antiparticles. this is a problem that's been studied a 164 00:13:33,210 --> 00:13:36,243 lot. The conditions under which this asymmetry 165 00:13:36,243 --> 00:13:40,998 could be formed using the known laws of Physics were formulated by Andrei 166 00:13:40,998 --> 00:13:44,539 Sakharov in 1967. the problem is called the problem of 167 00:13:44,539 --> 00:13:47,486 baryogenesis. There are many different models. 168 00:13:47,486 --> 00:13:52,529 The, I think the currently favored one is associated with baryogenesis via 169 00:13:52,529 --> 00:13:55,893 electogenesis. You generate an asymmetry in the lepton 170 00:13:55,893 --> 00:14:01,232 sector, which leaks into an asymmetry in the production of protons and neutrons. 171 00:14:01,232 --> 00:14:06,915 But this is an area of ongoing study, so there problems in cosmology that are not 172 00:14:06,915 --> 00:14:08,598 yet solved. That's fine. 173 00:14:08,598 --> 00:14:09,768 Something for you all to solve.