1 00:00:00,012 --> 00:00:03,601 And heavy lifting. Now we can put it together with the data 2 00:00:03,601 --> 00:00:06,596 that I promised you I would explain where we got. 3 00:00:06,596 --> 00:00:11,441 And understand, the history of the universe in the past and into the future 4 00:00:11,441 --> 00:00:16,111 because I said that understanding these parameters determines everything. 5 00:00:16,111 --> 00:00:20,252 Now, let's see how that goes and we'll talk along the way 6 00:00:20,252 --> 00:00:25,802 Early days of the universe, remember, early days of the universe would of been 7 00:00:25,802 --> 00:00:30,252 radiation dominated. I've talked about the fact that into the 8 00:00:30,252 --> 00:00:34,277 past, matter density increases like 1 / a^3 as a gets small. 9 00:00:34,277 --> 00:00:39,432 radiation density decreases like 1 / a^4. I didnt' say anything about. 10 00:00:39,432 --> 00:00:44,443 Dark energy density because remember that's a cosmological constant, that 11 00:00:44,443 --> 00:00:49,381 completely does not change the energy, the density of dark energy does not 12 00:00:49,381 --> 00:00:54,172 change with the scale of, factor of the universe and so this tells us, in 13 00:00:54,172 --> 00:00:59,086 particular, that if it's 74% of the energy density in the universe now, in 14 00:00:59,086 --> 00:01:03,753 the past when it was smaller and radiation and dust were denser, it was 15 00:01:03,753 --> 00:01:07,877 less important. So early in the universe the cosmological 16 00:01:07,877 --> 00:01:12,889 term plays absolutely no role and remember that the universe is radiation 17 00:01:12,889 --> 00:01:18,254 dominated until about 55,000 years of age and what does it tell me that it's 18 00:01:18,254 --> 00:01:23,972 radiation dominated? Radiation dominated basically tells me that Rho radiation. 19 00:01:23,972 --> 00:01:29,300 Behaves with the scale factor like a^-4, and so I plug that into the Freedmont 20 00:01:29,300 --> 00:01:34,424 equations and I find that the scale factor as I promised increases like the 21 00:01:34,424 --> 00:01:39,523 square root of time so the universe starts expanding very rapidly and then 22 00:01:39,523 --> 00:01:43,186 slows down. Of course this region over here where the 23 00:01:43,186 --> 00:01:49,952 universe is very tiny is, The beginning of this graph is something we will focus 24 00:01:49,952 --> 00:01:56,763 on a little bit later, but for the first 55,000 years of its universe, this is the 25 00:01:56,763 --> 00:02:00,686 plot of the scale factor as a function of time. 26 00:02:00,686 --> 00:02:05,927 I can sew this on To graph that describes the current universe. 27 00:02:05,927 --> 00:02:11,358 Of course here the scale is billions of years, so I've completely ignored the 28 00:02:11,358 --> 00:02:16,186 little tiny bit here that includes the beginning of the other graph. 29 00:02:16,186 --> 00:02:21,871 And so I've imagined starting at 0 With a matter dominated universe, things is, 30 00:02:21,871 --> 00:02:25,606 matter domination gives me the behavior I described. 31 00:02:25,606 --> 00:02:30,845 The scale factor increases like T ^2/3 and there's a transition from matter 32 00:02:30,845 --> 00:02:36,343 domination to domination by dark energy which remember, today there is about 3 33 00:02:36,343 --> 00:02:41,604 times as much dark energy as there is dust, remember I talked matter, dust, 34 00:02:41,604 --> 00:02:45,992 same difference. The transition occurs in the past when 35 00:02:45,992 --> 00:02:49,383 the density of dust was about 3 times what it is now. 36 00:02:49,383 --> 00:02:54,382 The density of dark energy not having changed, it would have been equal, and 37 00:02:54,382 --> 00:02:57,187 prior to that, dust would had been denser. 38 00:02:57,187 --> 00:03:02,992 That happened at a red shift of about. 0.4 or at an age of the universe of about 39 00:03:02,992 --> 00:03:06,622 0.6 of what it is now or about 8 billion years. 40 00:03:06,622 --> 00:03:12,282 And we see that over here and this heralds a transition from early times 41 00:03:12,282 --> 00:03:18,312 when the scale factor behaved like t to the 2/3, a power smaller than one, so 42 00:03:18,312 --> 00:03:22,765 that the, expansion was decelerating to the 43 00:03:22,765 --> 00:03:27,320 behavior at large times. At large times, as the scale gets larger, 44 00:03:27,320 --> 00:03:31,370 radiation has already been diluted to insignificance. 45 00:03:31,370 --> 00:03:36,988 dust also gets diluted to insignificance and what is left at large values of A. 46 00:03:36,988 --> 00:03:41,571 If the universe ever gets large And there is a cosmological constant. 47 00:03:41,571 --> 00:03:46,008 It will eventually take over. the expansion driven by a cosmological 48 00:03:46,008 --> 00:03:50,780 constant is an expansion where the right hand side of the Freeman equation does 49 00:03:50,780 --> 00:03:53,785 not depend on a, does not change with time at all. 50 00:03:53,785 --> 00:03:57,276 This gives us the closeset thing to a constant expansion. 51 00:03:57,276 --> 00:04:01,876 it's not a constant, expansion in terms of the rate of change 52 00:04:01,876 --> 00:04:06,623 of A it's a constant expansion in terms of the Hubble Constant is in this case 53 00:04:06,623 --> 00:04:09,771 constant. That means, remember the rate of change 54 00:04:09,771 --> 00:04:13,847 of A has to accelerate. In fact, it corresponds to an exponential 55 00:04:13,847 --> 00:04:18,688 growth of the scale factor and you can see that at late times as this term takes 56 00:04:18,688 --> 00:04:21,967 over. The curve turns over to an exponential 57 00:04:21,967 --> 00:04:27,252 rate, and because we have a non-zero cosmological constant or dark energy 58 00:04:27,252 --> 00:04:33,147 component, we predict that in late times we will have exponential expansion of the 59 00:04:33,147 --> 00:04:36,739 universe. We live right about here at 13.8 billion 60 00:04:36,739 --> 00:04:40,787 years where the scale factor by convention is exactly one. 61 00:04:40,787 --> 00:04:46,577 Notice we are not far from this turnover from the transition from dust dominated 62 00:04:46,577 --> 00:04:50,267 to cosmological dark energy dominated universe. 63 00:04:50,267 --> 00:04:55,647 We're at the region where expansion which had been slowing down is already 64 00:04:55,647 --> 00:05:00,282 accelerating This is the exact form of the function I've plotted. 65 00:05:00,282 --> 00:05:04,485 But more important is that it's exponential at one end and to the 2/3 at 66 00:05:04,485 --> 00:05:09,175 the other end and the remember way down here is a little region where it behaves 67 00:05:09,175 --> 00:05:12,636 like T to the 1/2. That, if you want, is the history of the 68 00:05:12,636 --> 00:05:15,790 universe. Note, that understanding the current 69 00:05:15,790 --> 00:05:21,058 parameter, cosmological parameters, once we figure out how to measure them, we can 70 00:05:21,058 --> 00:05:25,332 [UNKNOWN] the entire past of the universe and predict it's future. 71 00:05:25,332 --> 00:05:31,157 And we will see what all that means as a first application of all of these. 72 00:05:31,157 --> 00:05:37,577 Let's introduce this important issue not [UNKNOWN] related to oldest paradox of 73 00:05:37,577 --> 00:05:42,132 particle horizons. So how far can we see in flight space, 74 00:05:42,132 --> 00:05:44,302 normal space. You can see. 75 00:05:44,302 --> 00:05:48,973 All of the universe, that you just see farther and farther, but if you want to 76 00:05:48,973 --> 00:05:53,954 see things that are farther from you, you might need to look farther and farther in 77 00:05:53,954 --> 00:05:57,026 the past. But our universe, as Poe reminds us, has 78 00:05:57,026 --> 00:06:01,990 a finite age, so the question is, can we see the entire universe? What fraction of 79 00:06:01,990 --> 00:06:06,523 the universe can we see, and That fraction of the universe that we can see 80 00:06:06,523 --> 00:06:10,229 is called our particle horizon. And, it turns out that if you take any 81 00:06:10,229 --> 00:06:14,349 observer, of course all observers are the same, take some co-moving observer 82 00:06:14,349 --> 00:06:18,237 sitting at one point throughout the history of the universe, and ask what 83 00:06:18,237 --> 00:06:22,636 fraction of the universe He can see whether universe is infinite and we're 84 00:06:22,636 --> 00:06:27,571 going to talk here about a flag universe, remember i have a strong bias to a flag 85 00:06:27,571 --> 00:06:32,368 universe and i want to ask which other observers has he seen, okay and the aa, 86 00:06:32,368 --> 00:06:37,096 good way to describe this is, this is what we call the size of the observer by 87 00:06:37,096 --> 00:06:40,607 the universe. This is the distance from us to the most 88 00:06:40,607 --> 00:06:43,962 distant objects we have seen or can in principle see. 89 00:06:43,962 --> 00:06:49,012 These are the objects that we see so long ago, so far, that the light left them at 90 00:06:49,012 --> 00:06:53,052 the time of the big bang. So another way to ask the question is at 91 00:06:53,052 --> 00:06:57,937 any given time, what are the things that you see as they were at the time of the 92 00:06:57,937 --> 00:07:01,212 big? in time. And so the objects on the particle 93 00:07:01,212 --> 00:07:04,967 horizon are the things you see at the time of the beginning. 94 00:07:04,967 --> 00:07:09,822 Now of course in the radiation era for example you solve the equations and you 95 00:07:09,822 --> 00:07:14,602 see that the distance to the particle horizon increases with time [UNKNOWN] 96 00:07:14,602 --> 00:07:17,376 factor increases linearly as. Twice c t. 97 00:07:17,376 --> 00:07:23,386 So if you are looking at the universe a second after the big bang you can see two 98 00:07:23,386 --> 00:07:28,469 light seconds in each direction. Note two light seconds despite the fact 99 00:07:28,469 --> 00:07:31,449 that light is moving at the speed of light. 100 00:07:31,449 --> 00:07:37,346 How is this happening? Well remember this is the distance, now Coordinate distance 101 00:07:37,346 --> 00:07:41,004 at time 1 second. To those observers who's light you are 102 00:07:41,004 --> 00:07:46,370 seeing at time 1 second, from which light took 1 second to reach you but of course, 103 00:07:46,370 --> 00:07:51,100 in that 1 second those observers themselves moved so they are now 2 light 104 00:07:51,100 --> 00:07:55,171 seconds from you because expansion has carried them that far. 105 00:07:55,171 --> 00:07:58,332 In the matter of solving the same equations. 106 00:07:58,332 --> 00:08:03,849 You find that the objects you see, again ignoring the little bit of expansion 107 00:08:03,849 --> 00:08:09,568 during the small radiation era, in a matter dust dominated universe the 108 00:08:09,568 --> 00:08:14,705 distance that you can see all the way back to the big bang at time T increases 109 00:08:14,705 --> 00:08:18,476 with time as 3ct. You plug in that complicated function 110 00:08:18,476 --> 00:08:22,260 that describes. The transition region between dust 111 00:08:22,260 --> 00:08:27,618 dominated and dark energy dominated and figure out how far we can see today and 112 00:08:27,618 --> 00:08:32,902 again this is not how far the light has actually traveled, that's an ill defined 113 00:08:32,902 --> 00:08:36,211 question. This is how far today are the objects in 114 00:08:36,211 --> 00:08:39,622 today's coordinates are the objects which we see. 115 00:08:39,622 --> 00:08:44,654 As they were back at the Big Bang and if we could see them they would be 46 116 00:08:44,654 --> 00:08:49,349 billion light years away. Note this is a lot more than 13.8 billion 117 00:08:49,349 --> 00:08:53,233 light years. Light has traveled for 13.8 billion years 118 00:08:53,233 --> 00:08:58,847 but the objects that it left 13.8 billion years ago are now a distance 46 billion 119 00:08:58,847 --> 00:09:02,682 light years away from us so we can see, in principle. 120 00:09:02,682 --> 00:09:08,250 A big sphere around us whose radius today is 46 billion light years and that sphere 121 00:09:08,250 --> 00:09:13,564 is still growing but that growth stops in the sense that when you move to an 122 00:09:13,564 --> 00:09:18,956 asymptotic expansion, then at large times when we're describing an asymptotic 123 00:09:18,956 --> 00:09:23,992 expansion, the distance of the horizon becomes just a constant number. 124 00:09:23,992 --> 00:09:28,937 Some constant distance times the scale factor, so basically you're seeing the 125 00:09:28,937 --> 00:09:32,037 same objects. You no longer see, and once you hit 126 00:09:32,037 --> 00:09:37,102 exponential expansion more and more of the universe the ultimate limit, the 127 00:09:37,102 --> 00:09:42,057 things that we will see, out to the end of time, the most distant things we will 128 00:09:42,057 --> 00:09:45,273 ever see. Are those which are currently 62 light 129 00:09:45,273 --> 00:09:50,111 years away from us and anything that is currently farther than 62 billion light 130 00:09:50,111 --> 00:09:54,609 years, we will never see because the expansion of the universe carries 131 00:09:54,609 --> 00:09:59,658 themselves far, away farther away from us so fast from us that light from them will 132 00:09:59,658 --> 00:10:03,025 never reach us. So if you want this is the size of the 133 00:10:03,025 --> 00:10:07,883 universe we've observed so far. If, you, we had observed the universe, I 134 00:10:07,883 --> 00:10:13,279 don't know, 6 billion years ago, and you imagine that it was dust dominated, we 135 00:10:13,279 --> 00:10:16,096 would have seen about, half that distance. 136 00:10:16,096 --> 00:10:21,633 Because, in the dust dominated, world, the horizon distance grows linearly with 137 00:10:21,633 --> 00:10:25,251 time. And, it is, the growth, is, slowing down 138 00:10:25,251 --> 00:10:28,240 now. When I say half that distance, I mean, we 139 00:10:28,240 --> 00:10:33,772 would have seen half, that an eighth as many galaxies were visible, six billion 140 00:10:33,772 --> 00:10:38,268 years ago, as are visible now, assuming that galaxy density has not changed, 141 00:10:38,268 --> 00:10:42,597 which is probably false. and there's an ultimate limit to how much 142 00:10:42,597 --> 00:10:47,346 we will see, as I said when I discussed Olber's, it's not just that we have not 143 00:10:47,346 --> 00:10:51,012 yet seen everything, but even if we wait til the end of time. 144 00:10:51,012 --> 00:10:54,906 We will only see a finite extent of the universe. 145 00:10:54,906 --> 00:11:00,859 Only some finite chunk of universe. That chunk will grow but it will, we will 146 00:11:00,859 --> 00:11:05,035 only see a finite list of observers asymototically. 147 00:11:05,035 --> 00:11:10,722 You can ask a different question that defines a particle horizon, and here is 148 00:11:10,722 --> 00:11:15,524 drawn our particle horizon. is drawn in this dashed line as a 149 00:11:15,524 --> 00:11:19,515 function of time. And you see that indeed that's this 150 00:11:19,515 --> 00:11:22,782 dashed line over here as our particle horizon. 151 00:11:22,782 --> 00:11:28,121 at times from the beginning of the universe to 25 billion years, so right 152 00:11:28,121 --> 00:11:31,594 over here the horizontal line is where we are now. 153 00:11:31,594 --> 00:11:37,285 And these are at any given time all of the things, all of the parts, all of The 154 00:11:37,285 --> 00:11:42,574 galaxies if you want co-moving observers move, are at rest in this frame. 155 00:11:42,574 --> 00:11:47,864 They move along vertical lines so the dist, horizontal distance measures 156 00:11:47,864 --> 00:11:52,040 distance in two day's coordinate in today's s- universe. 157 00:11:52,040 --> 00:11:57,842 And so you see that we will see objects. bite, 25 billion years into the age of 158 00:11:57,842 --> 00:12:03,342 the universe we will have seen out a little bit past 50 billion light years 159 00:12:03,342 --> 00:12:08,817 and eventually this asymptotically ends at about, I said, 62 billion light years 160 00:12:08,817 --> 00:12:14,167 and by today we've seen out to about 46 billion light years despite the fact that 161 00:12:14,167 --> 00:12:17,512 the universe is only 13.8 billion years old and. 162 00:12:17,512 --> 00:12:21,889 That's one question you can ask. The other question you can ask is take 163 00:12:21,889 --> 00:12:26,868 today's universe, so think of this as a space time diagram, here is the universe 164 00:12:26,868 --> 00:12:30,110 of today, and say, suppose that something happens. 165 00:12:30,110 --> 00:12:35,161 Which of the events that are happening in today's universe will I ever see? And 166 00:12:35,161 --> 00:12:38,609 that answer turns out to be a different question. 167 00:12:38,609 --> 00:12:44,260 That defines something called our event horizon, so you can draw, and this is the 168 00:12:44,260 --> 00:12:48,822 picture of our event horizon. It separates, and that it turns out 169 00:12:48,822 --> 00:12:53,002 narrows with time. In other words these are of course. 170 00:12:53,002 --> 00:13:00,585 these are all of the events inside this which at any point in the history of our 171 00:13:00,585 --> 00:13:05,109 little corner of the universe will be visible. 172 00:13:05,109 --> 00:13:10,062 So if you want, this is the analog of our past light cone. 173 00:13:10,062 --> 00:13:13,992 At any given time. This is our light cone now, and if you 174 00:13:13,992 --> 00:13:19,132 add up all of the light cones into the infinite future, you get this event 175 00:13:19,132 --> 00:13:22,725 horizon. So, something that occurs today here, of 176 00:13:22,725 --> 00:13:28,468 course we can't see it, but if you give light time, will eventually, if something 177 00:13:28,468 --> 00:13:34,440 that occurs, say, here Today, of course we can't see it, but eventually someone 178 00:13:34,440 --> 00:13:39,821 on earth will be able to see it. Something that occurs, farther than 179 00:13:39,821 --> 00:13:45,554 about, what is it? About 15, 16 billion light years away from earth. 180 00:13:45,554 --> 00:13:51,657 Today, will never be seen, we can see the things that are 16 billion light years as 181 00:13:51,657 --> 00:13:57,847 they were in the past But we can not see anything that happens 16 billion light 182 00:13:57,847 --> 00:14:01,329 years away today. We will never, ever see. 183 00:14:01,329 --> 00:14:07,971 And in fact, because of the exponential growth, past once the cosmological term 184 00:14:07,971 --> 00:14:13,602 takes over, you see that our event horizon shrinks rather rapidly. 185 00:14:13,602 --> 00:14:19,202 And into the future eventually, if you ask, what are the objects that we will be 186 00:14:19,202 --> 00:14:23,902 able to see as they are 10 billion years from now, which is about here. 187 00:14:23,902 --> 00:14:29,952 You see, that they form a small fraction of the object whose, from today, which we 188 00:14:29,952 --> 00:14:33,327 will see. And, so, over time we get to see less and 189 00:14:33,327 --> 00:14:35,747 less. Of the universe in that sense. 190 00:14:35,747 --> 00:14:40,937 We get to see more and more of its past but if you ask say stars starting forming 191 00:14:40,937 --> 00:14:45,797 at some period over time we see less and less of the current history of the 192 00:14:45,797 --> 00:14:49,132 universe. an object and what you see is that over 193 00:14:49,132 --> 00:14:54,172 time a given object that is stationary say something 20 billion light years from 194 00:14:54,172 --> 00:14:58,192 us, well we could have see what happened to it at the big bang. 195 00:14:58,192 --> 00:15:02,892 We could have seen what happened to it at the age of 5 billion years, but by about 196 00:15:02,892 --> 00:15:06,792 10 billion years we lost it. Anything that happened to this object 197 00:15:06,792 --> 00:15:11,547 later than this point will never be seen at Earth so over time objects are leaving 198 00:15:11,547 --> 00:15:15,017 our event horizon. So what does that mean? Of course, they 199 00:15:15,017 --> 00:15:19,317 won't it's like an event horizon of a black hole it's not that they hit the 200 00:15:19,317 --> 00:15:22,739 event horizon. going to poof disappear what happens is 201 00:15:22,739 --> 00:15:27,059 that the light from this object experience an infinite, experiences an 202 00:15:27,059 --> 00:15:31,220 infinite cosmological red shift as it approaches the event horizon. 203 00:15:31,220 --> 00:15:36,017 Because essentially the time for light to get here becomes infinite, you get an 204 00:15:36,017 --> 00:15:40,252 infinite cosmological red shift and so we will see objects dimming. 205 00:15:40,252 --> 00:15:43,795 As they approach. So as the light from this object starts 206 00:15:43,795 --> 00:15:48,611 to reach us from bits of its history as it approaches the event horizon, we'll 207 00:15:48,611 --> 00:15:52,969 see it more and more and more and more and more red shifted, and it will 208 00:15:52,969 --> 00:15:57,829 basically dim itself out of existence, and of course we'll never see it across 209 00:15:57,829 --> 00:16:01,882 the event horizon. So we have our particle horizon Which is 210 00:16:01,882 --> 00:16:05,602 all of the bits of the universe that we can see. 211 00:16:05,602 --> 00:16:10,272 Since the big bang let me clear the picture up a little bit. 212 00:16:10,272 --> 00:16:16,792 So we have our particle horizon which currently at the present time involves, 213 00:16:16,792 --> 00:16:20,492 all the parts of the universe that we can see. 214 00:16:20,492 --> 00:16:26,649 As there were, at the Big Bang, this is our current particle horizon. 215 00:16:26,649 --> 00:16:32,352 Right, it touches, here. This is our current particle horizon. 216 00:16:32,352 --> 00:16:38,302 This is what we see is, we see all of this part of the universe. 217 00:16:38,302 --> 00:16:44,423 At some time after the big bang whereas in blue over here this is our current 218 00:16:44,423 --> 00:16:50,366 event horizon, these are all of the objects today that we will some day see. 219 00:16:50,366 --> 00:16:56,690 So in some sense with time we see more and more of the ancient universe and less 220 00:16:56,690 --> 00:16:57,351 and less.