How the Structure of the Universe Reveals Its Origins

0:00 We have a brochure from the right one. Very nice to meet you. Okay, I think it's ready to start here. It's very nice to see you all. and I'm delighted that Chris Isham and Gerald McCoy, I don't know quite how to pronounce that and John Leslie so kindly agreed to come so we have a wonderfully interdisciplinary group here to discuss that I think must be at least one of the most interesting three questions there are which certainly scrolls over into philosophy and theology as well as physics, astrophysics, and cosmology. When I was discussing this with Chris Isham, he joked that Joao would take the story up to the first, up to the plank time, and then he would take over from there. It was like, it's on my cheek. But I suppose it's the first plank time, which is where the deepest mystery really exists. But anyway, I'd like it to welcome Joao, from Portugal, and did a lot of his studies, in fact, in Cambridge, and is now based at the Imperial College. Thank you. So I was asked to review what we know for a fact about the origins of the universe. and what I shall be doing is mostly telling you what the basic trick is which allows you please just speak up a little

2:30 yes I think we can just turn the information sorry no don't worry I don't want to Sorry, yes. I'll try to shout, then. Yes, try to speak as loudly as you can, with comfort. Fortunately, my throat's not very good. Anyway. So anyway, what I will be doing is telling you what the basic trick is, which allows you to observe directly the universe as it was in the past. And after having introduced this setup which allows you to experiment with the universe, I will tell you what we know, what the observations are, what the well-established facts are about the origins of the universe. I won't quite go down for plenty of time, as promised. What I will do then is just describe the two main theories in modern cosmology which then try to explain the data. So there's a big difference between theories which don't try to explain anything other than concerns about what happens in the first point in time and the other theories which actually try to explain data. And it's the ones, the latter ones, which I'm going to concentrate on. One thing I should say from the start, and that is that if you look at the observations and you extrapolate them back in time, then you find that with minimal assumptions, You end up with a conclusion, the universe must have been created sometime in the past. There must have been a creation event in the past or a big bang in the past. And this is the reason why perhaps modern cosmology has become of interest in general beyond science, beyond cosmology. I think it's clear that modern cosmology impinges now on issues like religion and ideology. and a very good ground to see this particular connection is the cosmologists themselves as people the way they perceive this interaction I think it's quite curious if you look at the ex-Soviet Union where most of modern cosmology was produced and you can see that the people there the cosmologists who came up with these theories were under a lot of pressure

5:00 in a way to conciliate the idea of creation with dialectic materialism I'm not saying there was coercion, but in fact, there is some kind of back of your mind view that you should remove creation. And for this reason, non-minimal models like bouncing universes were introduced, which kind of shows some kind of interference of ideology, cosmology. A bouncing universe is a universe which doesn't start in the Big Bang. Rather, there was a collapse time before the Big Bang, which then bounced and exploded again. and we have a universe which just pulsates with an infinite series of cycles before the big bang and which therefore is not created. There are many more examples of this kind of interaction between science and other aspects of human and well for instance religion is the most important point I'd say and I think that although many scientists many cosmologists are atheists there's also a substantial amount of them who are not and I find two examples which represent two extremes connection between religion and cosmology in Joel Primack and Bruno Guidadone. The first one is Jewish, and he has the view that science is religion, according to the point of view that both kinds of endeavor try to find truth, and they have the same principles of ethics. The second, who is Muslim, believes exactly the opposite, that is his kind of compartmentalization of science creating a complete division between his work as a cosmologist and his beliefs and in this case you might think there is a bit of a schizophrenic approach to cosmology but there isn't he's actually quite the normal person and in fact this is another way to perceive this connection between science and belief so i think there is a variety of attitudes possible and the facts i'm going to tell you about certainly we're not concerned we're not they don't concern your personal beliefs and I think all this variety of examples show that that's much more a personal belief than a scientific matter another thing is of course the fact that the public in general has been interested in cosmology for the same reason for the same general reason we want to know how we were created and you probably heard that modern scientists to believe that universe is 11-dimensional, and it is a bubble. So I found it very curious to find

7:30 this cartoon, showing how somehow humor caught up with this idea. And you see everything here connected. You see ideas of religion, ideas of science, and ideas of humor all put together. And I think it's interesting, in general, I keep getting asked questions about what this theory of the universe means, and shall I read what this means? So beyond this introduction, let me just tell you what the facts are anyway, and why is it that the facts seem to confirm that we were originated in a big bang, in a creation event. So the basic trick is the following. Again, if you look out at decent objects like stars, you must realize that the way we see them is by means of light which they either emit or which they reflect. And if you combine this with the fact that light takes time to travel, you arrive at the conclusion that we are seeing these objects not as they are now when we see them, but as they were when they emitted the light we can see nowadays. So this immediately suggests a trick, which is if I want to look into the past of the universe, all I need to do is to look far away. Because in that case, I would be seeing the universe far away as it was in the past. And what this means is that, in a way, cosmologists are better off than archaeologists. We do not need, we do not need to rely on fossils or any kind of stuff processed by time. you can look directly at the universe as it was in the past simply by looking into this of course there is an assumption here which any philosophically oriented mind will catch up with immediately which is that I'm assuming that the universe looks the same everywhere that is the universe far away is the universe as it is here I cannot see the universe in the past as it is here but I can see the universe far away as it was in the past So this is really the basic trick, and the idea is just to find ways of looking further and further into the distance, therefore finding the universe further and further into the past to see what it shows. So scientists like very much to describe these things by means of diagrams, and I'm not an exception. I will be coming back to this diagram during my talk several times.

10:00 this is a kind of graphical representation of the trick which I just told you about it's called a space-time diagram it's a diagram which has space and is actually timing at axis and in which I define units of space and time so that light travels at 45 degrees so for instance if I were to define a unit of time as the year I should define a unit of space as the light year that is the distance traveled by light in one year So in this kind of picture, then you see that the sky is this blue line. If we are here, is there any point here, Austin? Don't worry. So if we are here, if this is the moment of timing we're at, if this is the moment of position of space we're at, if this is here and now, then what the sky is is just What the sky is, is just a sequence of shells corresponding to light emitted further back into the past and further away into distance. So the sky is not really this kind of two-dimensional thing which you might think it is when you look at it at night. What the sky is, is a complicated structure which basically integrates all these different shells and by looking deeper, what I can see is basically the universe further and further away. during my talk is essentially populating this diagram with the different times of the universe, the ingredients that you see at the different times of the universe, until I get to the creation moment. If you only use the naked eye, then what you see is mostly stars. And it is something which doesn't tell you much about the universe, because stars are very nearby. An important thing to make statements like this is to know what distance is. that I'm looking at distant objects and what their distance is. And this is a well-established branch of cosmology called cosmography, which is basically a ladder with many steps. The first step is quite easy to understand, and I'm going to describe it to you. So I can actually measure the distance of a star simply by using the fact that the Earth goes around the sun, and it's quite far away from this point every six months. So if I look at the star Say in January And if I look at it six months later

12:30 Then the angle at which the star appears Is different The difference in the angle Will be smaller and smaller Further and further away The star is So intuitively this is the same thing Which allows you to judge how distant Objects are in the landscape When you watch them in a train You see things further away moving slower Things nearby moving faster So by playing tricks like these, I can actually measure distances to objects which I can see. And I can therefore see or infer from the speed of light the time in the past at which they were. Most of the things I can see with the naked eye are, in fact, part of this structure which we call our galaxy, which appears much better in a different kind of frequency. These are three pictures of our own galaxy. And if I only use the naked eye, it looks as if the universe is indeed just an island and that there is nothing beyond this island, which is our own galaxy. So in order to kind of extend this view, extend this perspective, you need to use something like a telescope. Here's an example of a telescope. telescopes have been used since Galileo times they've been called instruments of the and in any case we've managed to extend our perception of the universe more and more so the more and more potent these things become so this is perhaps the most powerful instrument we've got so far it's in Hawaii for some reason it's always in nice places so that astronomers can have holidays after you and these things in particular this one has been crucial in establishing the basic truths of the Big Bang model so what you see by means of telescopes are things like other galaxies so what this gives you what this tells you is the fact that our galaxy is not the confines of the universe in fact it's just an island like many other islands which you can see We actually use telescopes, and that the basic unit is really the galaxy, that the universe is pervaded by galaxies, like ours. If you want to know the kind of distance scale you're talking about, let me talk in terms of the time light would take to travel across these structures.

15:00 So light would take about 100,000 years to travel across a galaxy, like ours, and 500,000 years to go in between one galaxy and another galaxy. Now, if you look even further away, and this is exactly where these kind of powerful telescopes become more and more important, you find the result that the galaxies themselves tend to cluster, tend to appear in groups, and this is an example of one, it's called the Comer Cluster. It's a very rich cluster, it has about 30, 50 galaxies. and again I have a repeat of the same story and I have when I went from the perception of my own galaxy and seeing more galaxies outside out there again our own galaxy is part of the cluster the local cluster and in general there will be other clusters which other galaxies belong and the cluster really is the unit where some kind of unity starts to appear in the universe so maybe it's not so clear in the optical like that. But in fact, clusters are really well-defined units. There is a kind of soup of gas, hot gas, which you can see in the X-ray. And it's kind of, the galaxies are a bit like peas inside this soup. And each cluster is really kind of a big wall containing some bits which actually shine and produce stars in their galaxy. Just to know what the scale of the cluster is now, then let me tell you what the numbers And for instance, something like the Koma cluster is so big that likely takes about two million years to cross the cluster from one side to the other. And as I said, the cluster level is really where the universe starts to show some unity. if I now make maps of different shells of the sky I see this I go further and further into the distance what happens is that my shell of the sky becomes bigger and bigger I also get a bigger and bigger sample of the universe and what I find is that the clusters start pretty much to divide themselves uniformly to spread themselves uniformly across the sky so they don't seem to be very uniformly distributed

17:30 inner most and closer to me is just because they're very small. I don't have a big enough sample of the universe. If I look far enough, then I would be at the bigger sample of the universe, and the picture which emerges is the picture of a pretty much uniform universe. So there are some oddities, and some people try to make theories using these oddities, but in general, the thing I'm about to show you is pretty unusual. This is a cannibal cluster. big cluster, which is basically eating up all the small clusters around it. But this is kind of an oddity, this thing is called the naval cluster. In general, clusters are pretty antisocial creatures, basically just keep themselves apart and spread themselves uniformly. So let me go back to my space-time diagram and give you the first insight into what the universe might be. if I only use telescopes then basically I stop being able to see beyond about 1 billion life years but the picture which emerges is a picture of a universe which is filled with this uniform soup of clusters clusters of galaxies nearby it seems it's not uniform but that's because I don't have a big enough sample if I go further away I get a big enough sample And the general image is that, in fact, it doesn't look as if the universe has changed very much in the last one billion years. So it looks as if this uniform soup of clusters has been around perhaps forever. And, in fact, there is a theory called the steady state universe, which made use of this fact and simply postulated a universe which was not only uniform in space, but also uniform in time. And therefore, you have a universe which is eternal. So the idea of an eternal universe really starts running into trouble with observations when you put into the picture another fact, which is that this soup of clusters is expanding, universes and all these clusters are receiving. They're moving away from each other. And in order to introduce that fact, I need to introduce it to a new effect, which allows you not just to compute the distance clusters, but also to find the velocity with respect to us. And this thing is called the Doppler effect.

20:00 So when you hear a train which is whistling approaching a station, you probably notice that there is a shift backwards in the pitch. Whereas when the train is going your way, there is a shift downwards in the pitch. And in fact, at this difference, the pitch is proportionally relative speed of the train. So I can actually measure the speed of a train making use of phenomenon. And this is the way planes actually measure their own speed. They basically use their radar signals and this docker effect to find the speed at which they're moving with respect to the ground. Now, galaxies are not loud objects, so I cannot use sound to measure their speed. But there is a similar effect with color, with light. So there is also a shift in color. If I look at objects which are moving towards me, they appear bluer. and they appear rather if you're moving your way. The effect is much more subtle because the speed of light is much larger than the speed of sound but it's a well-documented effect than less. So using this fact it was then noted by Hubble that the galaxies and plethora of galaxies appear rather which means that they're moving away from us. And furthermore fact that the speed of recession appears to be proportional to the distance they're at, the further away they are, the faster they seem to be moving away from us. And the relation between the velocity and the distance is one of proportionality. Now, this is really mind-blowing if you start thinking about it, because what this tells you is that we must have a big bang. And the reason for that is, if you consider a situation and I consider two galaxies, G1 and G2, then if this galaxy is moving away from me, then there must have been a time in the past when this galaxy was on top of myself, and I can compute that time simply by knowing what the velocity is and what the distance is. Now, the interesting thing is not only the galaxies which are moving away from me must have been on top of myself at some time in the past, but they must have all been on top of myself at the same time. And the reason for that is if the velocity is bigger for objects which are further away, then the two effects will counteract each other. So this

22:30 galaxy has more distance to move before it crashes on me, but it's moving faster as well. So if I rewind the film of expansion, I get the conclusion that not only each of the galaxies must have been on top of myself some time in the past, that at this time was the same. And this is really curious, because this is really what suggests the idea that there might have been a Big Bang some time in the past. In fact, if I know the proportionality constant, which is called the Hubble constant, relating to velocity and the distance, I can compute the time for the Big Bang, and this is about 15 billion years. So it looks as if, if I rewind what I see, backwards in time. It looks as if the universe was all concentrated in a single point 15 billion years ago and at this point exploded leading to the explosion I can observe nowadays. Excuse me, you're making the assumption that H is constant with respect to time. Yeah, I'm simplifying the argument. I'm simplifying the argument, of course. I'm simplifying the argument. You have to complicate this, but even so, you end up with the same argument, the same conclusion. So, I think you'll notice that, of course, the velocity cannot have been the same because there is a degravitational effect of the mass inside. This kind of sphere, I can imagine, on which I'm centered. So, this velocity must be accelerating. The velocity was larger in the past. It's actually the other way around. It's worse. It's actually the opposite. The 15 billion years of age is actually what we call an upper limit. It's actually less than that. So, the time for the big bang is less than that. So, are the accelerators and the accelerators? What do I actually do? Not with accelerators. In the past, it's people's lives. so it's just as well you caught up with the fact it was a simplification next time I will actually put the full argument there I'm avoiding equations I said the only equation I would put in this talk is velocity equals space of a time which is what it was and of course it's more complicated than that

25:00 there's a fact that this acceleration comes from It can actually be derived just from Newtonian gravity. I could go through that, but I decided not. So anyway, even so, there are ways around the idea of the Big Bang. And the steady-state universe survived for a while and explained expansion as well. But you must make very non-minimal assumptions for that to be true. And in fact, what the steady-state universe postulates is that there is creation of matter at any time. And what this means is that the cosmological expansion is not diluting the universe. And similarly, if I look backwards in time, the universe will not have been more concentrated. So the density of the universe in a steady-state universe is in fact constant, and the universe looks the same at any time. and I can actually explain expansion and still have an eternal universe but the price I have to pay for that is introducing new physics in particular violating conservation of energy you can do that if you want the other picture though and the reason why I think I think the reason why the steady state universe kind of was appealing to this favor is because it also paints a picture of a universe which does not evolve which looks the same at any time. And for a long time, this was actually consistent with observations, as I told you. There's no reason why, if you just look at this cluster soup, why this cluster soup should have been different at any time in the universe. The big revolution really came with these things called radio telescopes. You probably remember these things, associated with Johnny Foster, somewhere in the film Contact. These things are actually not used to look out for extraterrestrial life. They might be in the future, but they haven't been so far. What these things are used to is basically to push the boundary of what I can see using normal telescopes. These things are really huge. I mean, just to give you an idea, each of these antennas is about 40 meters across. And this is the full array of antennas, and they're all looking in the same direction. And what these things do is basically use a technique which allows you to resolve a gold ball about 200 kilometers away. so it's basically what they can do is resolve things which appear very small in the sky and therefore things which are very far away

27:30 and if you point this thing at the sky which was done in the 50s late 50s and 60s and you find something shocking which really killed the steady state universe you find that the universe very very far away is actually not made up of clusters of galaxies it's made up of quasars And just by looking at this picture, you'll see this doesn't look anything like a galaxy. So there's this different kind of animal. In fact, these things emit much more light than a galaxy. They emit about a thousand more times in a cluster. And they're also, well, the shapes and kind of the various interactions they've got are all very different. It's very clear there has been some evolution in the universe. In a way, these things are the precursors of galaxies, things which were around before galaxies emerged. These things are about 5 billion years old As opposed to the further clusters Which are 1 billion years old So let me complicate my space-time diagram And so what the optical telescopes gave us Was these last 1 billion years Of the universe And the picture I got is a picture of a set of clusters In the common street If I go five billion years back, I find a different generation, I find the quasars dominating the universe, again, pretty much uniformly. So if the universe is evolving, really, one of the main predictions of the steady-state universe is not true. And if I drop the steady-state universe with this extra assumption of energy conservation violation, then I must have a big bite. So, you might ask at this point, how far back can I explore using this trick of just looking far away? And one thing which is important to realize here is that universes with a creation event have an horizon effect. So, my sky must necessarily be truncated somewhere. There must be a distance beyond which I cannot see anything because it would correspond to to emission of light before the Big Bang, before the creation. In fact, it looks as if I live inside a cavity and the kind of the edges of the cavity is revealed directly by observation.

30:00 A Big Bang. If I'm in the center, there will be this kind of cavity which is about 15 billion years, light years, across. And if I look through it, I should be able to see point, the Big Bang itself, the creation event itself. Of course, this is too good to be true. And what happens is a complete disaster. And the disaster is that there is a time back in the past when the universe was so concentrated it became opaque. So if the universe is expanding, it's getting diluted, this means back in the past it was more concentrated. it means there must be a time when light is just going to travel freely the universe is transparent nowadays which is why we can see things far away but there must be a distance corresponding to a time when the universe is optical or if you want, for light so play so this is a bit tantalizing because I can't really quite see the big line I can see at most this thing this edge, which is called the optical horizon You might wonder what kind of light is coming out of this optical horizon. This is called the cosmic microwave background or the cosmic radiation. So the cosmic radiation is very important because it represents the limits of this kind of search into the past with current technology. It represents the further into the distance, the further into the past I can actually see directly. Beyond the cosmic radiation, this is pure speculation because I can't see directly what's going on. This is the final rendition of the picture as it is nowadays. This is us, this is the epoch of clusters, this is the quasars, and then there is the cosmic radiation emitted. And I can't see beyond this point because the universe is opaque. If you want to know the kind of time scale on which these two events occur, I told you the universe is about 15 million years old. This event occurs about 100,000 years into the life of the universe. It's not a big tragedy. I mean, if you compare these two numbers, this is pretty much the initial conditions of the universe if you want, but it is not a big bang. I should say this is a limitation of current technology. there's no reason why other radiations should be, should find universal plates before this time. And in particular, if I could build a telescope which could see gravitational radiation,

32:30 I could see it through this barrier. But this is well beyond current technology. In fact, we have not even yet detected directly gravitational radiation. Unless there is no, there is nothing in principle which should prevent us from seeing the big man. Just current technology is not good enough for them. So at this point, let me tell you what currently is possible, what is actually, what do I see when I look at cosmic radiation. So at this point, you really need to go into space. This is where your tax money goes into. And this is the COVI satellite, which really started the revolution because it gave us some of the best pictures of the cosmic radiation. and these things are really the prime ground for testing theories of the early universe because of course they show a picture of the universe as early as I can see so what do I see well what I see looks a bit boring actually so what you see is basically just a uniform sea of radiation which is about 3 degrees above zero this radiation is not quite uniform with weather. In any case, it's actually quite, I mean, you might think it's boring, but it isn't, because in a way, this is a confirmation that the universe is homogeneous. So, in a way, this thing is telling me that the theories, which are the simpler theories, are actually the right theories, because if I look far enough, and this is the largest sample I can possibly have of the universe, because it's the outermost shell I can see in the sky, If I look at this shell, it looks uniform. If it was completely uniform, this would be a bit of a problem, because then I could not possibly explain the formation of galaxies. What the COBE satellite did was to show that on top of this near uniformity, there are self-situations indeed. Keep coming. Sorry. It's okay. So anyway, it's important that, in fact, the thing is not just nearly uniform, but also

35:00 it has some small fluctuations. And to give you an idea of how small they are, they are about one part, the 100,000. So it's very, very small fluctuations. What these things are, are the progenitors of what later on becomes quasars, and then later on become galaxies. So the picture which is emerging at this stage is a picture of the universe which is fairly homogeneous but not quite, and the not quite is what allows us to be here, as some small in homogeneities, which can grow into structures, and the universe on very large scales is homogeneous, but on very small scales is very structured. It's actually quite curious that you can reject lots of other models of the universe, namely non-homogeneous models of the universe and for instance before the COVID picture appeared rotating universes were very popular. Unfortunately this is the kind of microwave background they could eat It's a very beautiful picture, which doesn't correlate very well with these other pictures and this is the reason have once again disappeared. So it looks like the Big Bang model, the idea that universe is homogeneous and expanding and started in a creation event, is a model which seems to be fitting the data better and better. And at this point, I will finish with the observations and I will start with the theory, but let me just review, before I leave the observational grounds, let me just summarize what we know for a fact about the universe. So what we know for a fact is that the universe is expanding. And if I rewind this expansion back in time, it looks as if the whole universe started in one point in a big bang, in a creation event. And the second striking feature which I observe is that the universe is homogeneous, but not quite. I mean, on bigger scales and very early on, of genius, but then later on structures appear and grow on very small scales. So beyond these observational facts, then are the theories. How am I going to explain these various things? And the two things, the two main features I'm going to concentrate on are the homogeneity of the universe and the small fluctuations. How do they come about? And what I will be doing now is just reviewing the two main candidates for explaining these

37:30 inflation and topological defects. I should say, observations finished here. From now on, it's just theory. So I will start with inflation. One of the main paradigms in cosmology in the past 20 years or so has been inflationary universe. And the idea is to kind of complement the big-point model with something which happened very early on, maybe just after the planet. And which enables you to explain the homogeneity of the these small populations in the universe, which is essentially homogeneous. You can't explain the homogeneity of the universe in a standard Big Bang model because of a very curious effect, which is called the horizon problem. So I told you earlier on that the fact that there is a creation event in the universe means there are horizons. And nowadays, I can't see beyond a certain distance because the universe didn't exist before. But the thing I should have said is that, of course, the horizon is increasing in time. The older I get, the more and more of the universe I can see. Reciprocally, if I go back in time, at the very young universe, the universe hasn't lived much yet, so observers can only see a small fraction of the universe. The horizon was very small in her early universe. so what this means is something which is really tragic which is, if I look now back in time I can see regions which don't know about each other because they're outside each other's horizon and I can compute in fact how big the horizon is when the cosmic radiation was emitted and it is tiny it's about the size of the moon about two sizes of the moon it's about a small bit of this matter about this size so I observe it on my path the emission of the cosmic radiation and all these areas are in fact disconnected from each other, completely ignorant of each other completely outside each other's horizon and you see that this immediately precludes explaining the homogeneity of the universe in a big bang model I cannot have any equilibration mechanism ensuring homogeneity if I don't have any contact between the various portions of the universe very early on So this is really what made inflation become so popular Inflation is a way around the horizon problem Inflation is a way of connecting the whole observable universe very early on

40:00 And the idea behind inflation Is that the expansion was not always accelerated So I told you earlier on As a sad remark actually That the expansion of the speed at which things are moving And the reason for this is that if I consider myself to be here and I look at some point which is receding with some speed, then you must consider also that there is the gravitational interaction of all this matter on this point here. And what this means is that there is the acceleration in the expansion of the universe if I have attracted gravity. So what inflation does really is postulate, and I should stress this, it's just to postulate early universe there was a period in which gravity was repulsive. This is not as far-fetched as you might think it is. In fact, there are many theories, field theories, which predict this kind of gravity. It's just kind of an unusual matter. It's a thing called the inflaton. And basically what inflation postulates is a period in the early universe where I'm dominated by this field called the inflaton for which gravity is repulsive. So what this The reverse of this type of expansion may have actually accelerated expansion. If I look at an object very far away, it is moving at the curve and speed, which is increasing more and more because this piece of matter here, rather than trying to hold it back, I actually try to get rid of it by the repulsive effect of gravity. if you combine this with another effect which I'm going to tell you about then you can actually solve the horizon problem and there is a very curious effect in expanding universes which is that the distance I travel is actually smaller than the distance from the starting point and the reason for this is if I'm here the universe is expanding and I start moving then the expansion of the universe stretches the bit which I've already walked in the past. And because of this, the distance from the starting point is always bigger than the distance I've traveled, because expansion keeps actually interacting, keeps acting on the distance I've already traveled. So this is a very curious effect, which you only have in expanding universes,

42:30 and which means if I look at light and the way light travels in a given time t, You might think, like in one year, you might think light travels one light year, but in an expanding universe, it actually travels much more than that because of this effect. Currently, light actually travels something like two light years. And the key point about inflation is that if the universe is expanding very fast, then this effect is completely over the top. And we, in fact, end up effectively with an early universe, which is completely dominated expansion. So this is a very curious effect, which is behind the solution of the horizon problem in inflationary universes. What this means is that effectively, if I don't take into account that expansion could have been accelerated, it looks as if the speed of light was much bigger in the early universe. And of course, in the previous picture, which I gave you, it was a bit as if there were all these small horizons because the universe had only lived a tiny bit. But in this kind of case, if the speed of light was indeed much bigger, in fact, the horizon was much bigger in the early universe. So what inflation does is basically postulate the period very, very early on, very first fraction of the universe, in which things were not as they are now, in which expansion was not accelerated, in which it was accelerated, in which the horizons didn't grow the way you think they grew, they grew much faster. And by playing this trick, you can actually say that the whole observable universe nowadays was in fact all connected initially inside one horizon because of inflation. So this is really why inflation has become one of the main paradigms. It kind of complements the Big Bang model, allowing one of its main features to be explained by comfortable processes. If you solve the horizon problem, you can now solve the homogeneity problem of the universe. You can explain why some equilibration mechanism very early on could actually have acted all across the universe beyond what you might think were lots of disconnected horizons and made the universe look all the same. So inflation can do many more things, and I'm only going to mention a few. Inflation can do things like explain also to the small fluctuations around homogeneity.

45:00 And this is really the bit of inflation which is more interesting for observations because what we want to do is explain the small fluctuations in cosmic radiation, to explain the structures, the clusters, the quasars you observe nowadays. And the way in inflation you explain the small fluctuations is exactly by the fact that if you have this accelerated expansion, you can convert very, very small scales, scales into very, very big scales, macro-physical scales. Now, we know that quantum mechanics doesn't let you predict perfect homogeneity. There must always be some quantum fluctuations on very, very small scales, micro-physical scales. And that should not affect cosmology at all, because we're talking about smallest scales. What inflation does, in a way, is convert these tiny scales into, say, the scale of a cluster. so inflation really is quantum mechanics what originates later on the structures of the universe you can see nowadays and it's a very predictive theory as a matter of fact, it can actually predict very concretely what kind of spots I should see in the microwave in the cosmic radiation and what kind of property the cluster distribution should have I didn't want to go too much into the details of inflation Tomorrow, we'll be talking about fine-tuning problems. Let me say that inflation also solves many fine-tuning problems. And this is really not inflation as a theory of what we can observe. It's inflation as a theory to kind of explain metaphysical things. And this is not the derogatory I've spent the last six months working on metaphysical things. But let me just tell you what these things are anyway. So let me go back to this picture in which... Thank you.