Skip to 0 minutes and 14 seconds We have seen that the great homogeneity of the cosmological microwave background– discovered by Penzias and Wilson and studied by the COBE satellite– is causing problems with causality. This is summarised by what one calls the horizon problem, which is the following. Why is it that two points in the sky which are too distant to have exchanged any information since the Big Bang could have exactly the same properties? To solve this puzzle, theorists have introduced a very primordial phase of evolution, which is called inflation, during which the Universe was in very fast, one even says exponential expansion. And so an important question is raised.

Skip to 0 minutes and 59 seconds Is there any observation today that could test this phase of inflation and so could probe the first instants of the evolution of the Universe?

Skip to 1 minute and 13 seconds We have seen the importance of the quantum vacuum in the context of inflation. So let me try to focus a little more on this important notion. In everyday language, the vacuum is what remains when we have taken everything away. Now in the quantum world, things are a little different. So let me try to explain that. There’s a possibility that there is a pair of particle-antiparticle which is created out of a vacuum. So let me take an example. I have here a production of an electron and its antiparticle, the antielectron.

Skip to 2 minutes and 3 seconds Now the electron has a mass. Let me call it m. So it has an energy, mc squared. And the antielectron has the same mass. So it also has an energy, mc squared. So it seems that out of a vacuum, we have produced an energy mc squared plus mc squared, 2mc squared. So it seems to be in contradiction with the conservation of energy. Now quantum physics tells us that this is allowed as long as it lasts a very small amount of time, a microscopic time. So time is flowing in this direction. And this violation of energy is allowed for a very small time, a time which is smaller if the mass is larger.

Skip to 2 minutes and 54 seconds So that means that that fluctuation is allowed as long as, after some microscopic time, the electron and the antielectron annihilate again into the vacuum. And so you see that quantum fluctuations of energy are allowed for a very small amount of time. Now this happens here, but in the empty room, there will be another fluctuation here, another fluctuation here, and so on everywhere. And so that means that even though each individual fluctuation is lasting a very small amount of time, on the average, they will be contributing to the energy. This is what we call the energy of the vacuum. And this is precisely this energy that is the engine of inflation.

Skip to 3 minutes and 55 seconds I’ve mentioned the word antiparticle, so let me say a few words about antimatter, which consists of antiparticles. As a matter of fact, there is very little difference between a particle, like the electron in my example, and its antiparticle, the antielectron, which we sometimes call the positron. The only basic difference is that one has a charge which is negative, the other one has a positive charge. Otherwise, there is basically symmetry between particles and antiparticles. Now of course, there is obviously a dissymmetry in the Universe because we know that our observable Universe is made mostly of particles. So the question is, why? This is what we sometimes call the matter-antimatter asymmetry.

Skip to 4 minutes and 45 seconds Now there are theories that tell you that there are tiny differences between particles and antiparticles which started an unbalance between matter and antimatter in the early Universe. And that, little by little, evolved into our present Universe where matter is completely dominating the observable part of our Universe. There are very interesting theories explaining that. Although none of these theories has led to any prediction which could be, at this point, tested. So this question of the matter-antimatter asymmetry lies a little outside the main purpose of this course, which is gravity, and so we’ll leave it as it is for the timing being.

Skip to 5 minutes and 38 seconds Let me describe in some detail the inflation scenario. Before I do that, I would like to take an example that might be useful when I discuss it in detail, which is the example of a roller coaster. Just imagine that you’re on a roller coaster. So you started from the ground. You have been climbing, so you have been accumulating some energy, some gravitational energy. And then you restitute that gravitational energy, mostly in the first fall, and then when you go round, and round, and round, but more slowly, up to the end of the roller coaster. Well, the evolution of a Universe during inflation is a little like travelling on a roller coaster.

Skip to 6 minutes and 26 seconds So let me explain this in more detail on the board. I will represent the evolution of energy with respect to time.

Skip to 6 minutes and 39 seconds So energy is plotted here with respect to time. At the beginning of inflation, a large amount of energy has been stored in the vacuum. So this is here, vacuum energy.

Skip to 7 minutes and 4 seconds And for some time, the energy of a vacuum would be large until we move to another vacuum of much lower energy.

Skip to 7 minutes and 19 seconds Now in this first spot, we have stored gravitational energy in the same way that at the top of a roller coaster, we had also stored some gravitational energy. And so that gravitational energy of the vacuum will trigger a very fast evolution of the Universe, this fast evolution of the Universe that is characteristic of the inflation here. At some point, we drop out of this state to fall into a second vacuum. This is where information is stopping. So this part here corresponds to inflation. And then we’ll restore the energy to the second vacuum. So we’ll be falling into the second vacuum. And from then on, the evolution of the Universe is much slower.

Skip to 8 minutes and 21 seconds This is the kind of typical Universe that we live in today.

Skip to 8 minutes and 34 seconds Now I have said that the energy of the vacuum is due to the vacuum fluctuations. So that means that on the left-hand side of the diagram, one has the full energy of the vacuum, this is constituted of the many different fluctuations. And so because these fluctuations are different in different parts of spacetime, that means that the energy will not be exactly identical in all parts of spacetime. And so we expect that the height of the energy, of a vacuum energy, will be different in different parts of spacetime. And so inflation will be slightly different in each part.

Skip to 9 minutes and 15 seconds And so we expect, when we get out of the inflationary phase, when we get to the right of the diagram, that different parts will have inflated a little differently. And we expect some fluctuations in the cosmic microwave background.

Skip to 9 minutes and 35 seconds How do these fluctuations appear in the cosmological microwave background? We have to remember that at the time of recombination, just before recombination, matter and light, matter and radiation were tightly coupled. Moreover, we have seen that the horizon at that time was much closer, much smaller than it is today, about a factor 1 over 1,000. Now that means that you could imagine matter and radiation tightly coupled inside a box, which would be the causal horizon. Now there are two different effects. One which was gravitational attraction, which would tend to get everything tighter. The other one had to do with radiation. You may have seen these radiometers, which are these small instruments where the sunlight keeps moving a small helix.

Skip to 10 minutes and 36 seconds Well, the effect of light is to try to push everything out. So there are two contradictory effects– one, a contraction, the other one, an expansion. And so that led to oscillations of the same type as acoustic oscillations inside the box of the causal horizon. And so the situation is somewhat similar to what happens when you put a conch shell to your ear– a small noise outside is turned into the sound of the sea inside. Because this is acting like a box, and there is resonance inside the box.

Skip to 11 minutes and 15 seconds Well, similarly, the small fluctuations which are due to the phase of inflation– as we have seen, the fluctuations of the vacuum– are turned in the box of the horizon, where you have this coupled matter-radiation, into larger fluctuations, at least fluctuations that could be seen. And so we expect some fluctuations in the cosmic microwave background, fluctuations which were observed by the COBE satellite.

Skip to 11 minutes and 51 seconds And indeed, a team led by George Smoot, with whom we’ll be discussing about his discovery in the next sequence, identified these tiny fluctuations in the cosmic microwave background. So the cosmic microwave background is very smooth, very identical everywhere. But in 1 part into 100,000, there are tiny fluctuations. Now since the discovery of COBE, there has been more detailed, more refined maps of the cosmic microwave background. You have one here. which sort of summarises the map of the whole sky, of the cosmic microwave background. So you see that you have tiny fluctuations. The blue dots are of a little less energy than the red dots. The difference is just 1 over 100,000.

Skip to 12 minutes and 45 seconds And you see here, a red structure this is just our own galaxy. So if you suppress our own galaxy, if you subtract it, then you’ll get a map of the primordial fluctuations, the primordial fluctuations of the cosmic microwave background. Nowadays, the Planck mission has provided us with an even more detailed map, which is here in the background. And so you see that by analysing the fossil radiation of these fluctuations which date back to 380,000 years, we might get clues about the behaviour of the Universe at that time or even earlier during the inflationary phase.

# Looking for anisotropies of the cosmological background

If inflation explains some of the mysteries associated with the homogeneity and isotropy of the CMB, it also leads to some observational predictions. In order to understand them, it is important to investigate the central role played by the *energy of the vacuum*. This is the first time that we encounter this central notion: the energy of the vacuum is due to the quantum fluctuations of particles. And these fluctuations will eventually lead to fluctuations, or anisotropies, observed in the cosmological background. An indirect way to observe the vacuum… (13:45)

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