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Skip to 0 minutes and 14 seconds There is a question which is often asked to us cosmologists which has to do with the fact that we live in a very large Universe. If there are parts in the Universe which are currently out of reach– we have seen that we can see as far as 14 billion light years– what about if the Universe is infinite, there are parts that will never be within our reach? Should we take those parts into account or should we just ignore them? I will bring different elements of answers to this question and we’ll see that this very important question has many interesting aspects from the point of view of cosmology.

Skip to 0 minutes and 59 seconds The first element of answer– the horizon on Earth. Everybody’s familiar with that line that separates the sky from the Earth– for example, when you’re at the ocean. And that horizon– it’s actually a Greek word which means “to set a boundary,” “to set a limit.” This line of the horizon was very important for the Greeks indeed. That allowed them to understand that the Earth is a round object, a sphere, because you see boats disappearing at the horizon or appearing at the line of horizon, so that means there is a surface of the Earth beyond.

Skip to 1 minute and 40 seconds And so you see that that notion of horizon is the one that tells you that something about the geometry of the surface of the Earth, the fact that it’s a sphere, you can deduce that from the fact that precisely you see boats disappearing at the horizon.

Skip to 2 minutes and 4 seconds Second element of answer– causality. Causality plays a very important role in cosmology, especially when we discuss the boundaries, like the horizon. So what is causality? It’s just the familiar statement that a cause always precedes an effect. So let me illustrate this on some event in space time. Let me consider event number one. Einstein, in the fall of 1915, publishes his paper, his famous paper on general relativity. So it’s an event in time and space. So that’s event number one. Event number two– this morning, I spilled coffee on my gravitation book. That’s an event, again, in space and in time.

Skip to 2 minutes and 54 seconds Now, you could imagine that Einstein publishing his paper on general relativity, which is the subject of this book, might have some influence on my spilling coffee. For example, I was immersed in the reading of this book this morning and I didn’t pay attention to my cup of coffee. It’s impossible that my spilling coffee on this book had any influence on Einstein writing his general relativity paper. And so, you see that… that’s a very simple example of two events and the sort of order between the two. The two are not playing the same rrole with one another. The one in the past has some influence on the one now, or events in the future.

Skip to 3 minutes and 40 seconds So we’ll come back to that, but that notion of causality is playing a very important role when we discuss cosmological issues.

Skip to 3 minutes and 51 seconds Let us consider this event number one, Einstein writing the theory general relativity and publishing it in the fall of 1915. That’s 100 years ago, so the information was sent out to the cosmos and has reached only a region of the Universe which has a size of 100 light years. Anybody who is living outside this region of radius 100 light years from the Earth still doesn’t know, could not possibly know, that Einstein has written, has published this paper on general relativity. Now conversely, information from the rest of the Universe reaches us if it took less than the age of the Universe to reach us.

Skip to 4 minutes and 40 seconds So that means that we can only get information from around us, from a sphere which basically has a distance of 14 billion light years. Anything that is beyond those 14 billion light years is out of reach. No information can reach us, even if it started at the beginning of the Universe. And so you see that there is a notion of cosmological horizon– information cannot reach us, just the same way as in the terrestrial horizon.

Skip to 5 minutes and 14 seconds You know, the boat which was beyond the horizon could not let us know that it was coming towards us, while similarly, anything that happened in the Universe beyond the cosmological horizon at the radius of 14 billion light years cannot reach us in time for us to know anything about those parts of the Universe.

Skip to 5 minutes and 40 seconds Now, things are a little more complicated because we live in an expanding Universe. So we have to take into account the expansion of the Universe when we discuss horizon. And if you do that, then you soon realise that the size of horizon is also expanding with the evolution of the Universe. And so this means that when you run the Universe back in time, as we do when we watch the sky, the size of the horizon is diminishing with the distance. Now, if we look at the photons from the cosmic microwave background– from the CMB– we look at the time which is 380,000 years after the Big Bang. And so, at that time, the horizon of those photons was much smaller.

Skip to 6 minutes and 36 seconds To give you an idea, an order of magnitude, if you look at the sky and if you look at your fingers, making at an angle of one degree. So if I look at the sky, two points separated by an angle of one degree, then that gives you the order of magnitude of the horizon at that time. And so comes a difficult question which was at the basis of the understanding of the cosmic microwave background. If the horizon at the time of recombination– 380,000 years after the Big Bang– was this size on the sky, that means that photons coming from this direction and coming from this direction, say at a 30-degree angle, should not be correlated.

Skip to 7 minutes and 26 seconds So these correspond to Event One, these correspond to Event Two, and there is no causal relation at the time of the emission of these photons between these two events. So why does the CMB have the same properties all over the sky when these photons, when they were emitted, could not have exchanged any information since the beginning of space time? So this is a very difficult question, and to try to answer this question about causality led theorists to introduce a new theory and a new era in the evolution of the Universe.

Skip to 8 minutes and 14 seconds Indeed, in the ’80s, theorists from particle physics invented a scenario called inflation. That’s a scenario of extremely rapid expansion of the Universe in this very early phase.

Skip to 8 minutes and 29 seconds The expansion is so rapid that distant parts of the Universe recede from one another at velocities larger than the speed of light. One talks about supraluminal expansion. Now, you might immediately think that this is forbidden by Einstein’s theory who tells us that there is no motion of any objects beyond the speed of light. Now first, you have to consider that those galaxies– or, at the time, there were no galaxies. Those different points of the Universe are receding from one another because time and space are expanding in between. And let me also give you an example by returning to our example of the Universe seen as a balloon.

Skip to 9 minutes and 20 seconds Remember the Hubble law that was telling you that the velocity at which objects recede is proportional to their distance. So I’ve got here two different objects at a rather small distance. But you imagine that if I increase the distance very much– for example, between these two objects– then there is a distance at which they will recede from one another at a velocity which is larger than the speed of light. Now, does that mean any contradiction? Not necessarily. That just means that information can no longer travel from this point to this point, because in order to connect this event with this one, that would mean that it has to go faster than the speed of light.

Skip to 10 minutes and 8 seconds So space time is inflating, these two points recede from one another at a velocity larger than the speed of light, and information can no longer be communicated between these two events.

Skip to 10 minutes and 25 seconds Let me now explain on the whiteboard how the scenario of inflation is a help for understanding the causality, the causal connection, between the photons of the cosmic microwave background.

Skip to 10 minutes and 42 seconds So I have presented here the evolution of the horizon during a scenario which starts with inflation and then gets back to the standard evolution of the Universe. During inflation, it turns out that the size of the horizon is constant. Then when we get later to the standard evolution, we have seen that the horizon is slightly increasing with time. So you see a slight increase that goes on. Now, during the inflation, the Universe is starting… at least what we call the “observable universal,” the Universe that we see today, which is 14 billion light years around us. … that observable Universe was a tiny dot inside the horizon.

Skip to 11 minutes and 37 seconds And then it suddenly expanded to something, some region that was starting to be much larger– or at least, larger than the size of the horizon. And then we come to the standard evolution, and that Universe has continued expanding. This is the expansion that we see now, and so it’s even bigger. But you see that this type of scenario, adding an inflation era helps us understand, for example, the disconnection, apparent disconnection, between photons of the CMB at different degrees, different angles, because all these are coming from the same… So for example, these two regions were inside the visible Universe, this tiny point at the start.

Skip to 12 minutes and 37 seconds So they were in causal contact because they were inside the horizon at that time, and so that means that because of this rapid expansion of the Universe, they are now also in causal contact. They could talk to each other in that very early phase.

Skip to 12 minutes and 55 seconds Two precisions concerning the scenario of inflation. The first one is that you should not confuse the Big Bang and the epoch of inflation. The epoch of inflation is following the Big Bang. In the case of the Big Bang, our equations do not apply, there is a singularity. We don’t know exactly what’s going on. In the case of inflation, as we will see next time, we have a theory of inflation. So this is completely within the sort of validity of our theory. We can describe that period of inflation and make predictions.

Skip to 13 minutes and 30 seconds Second thing about inflation– precisely because this is a very rapid expansion of the Universe, any kind of curvature, sign of curvature in space will just be smoothed out by this almost explosive expansion. And so, when we get out of inflation, we are in a Universe where, basically, space is flat. So there is no sign of curvature anywhere, everything has been smoothed out. Now, you might be a little confused because I spent quite some time convincing you that space time is curved, and now I’m saying that at the end of inflation, space is flat.

Skip to 14 minutes and 13 seconds So in order that you understand that this is not contradictory, let me take a very simple example of this sheet of paper which I turn into a cylinder. And you see, for example, in the case of this Universe, there is a flat direction. There is another direction which is a circle, which obviously is curved. So that gives you the idea that at least space could be flat, even in a curved space time.

Skip to 14 minutes and 48 seconds To summarise, we have introduced the scenario of inflation in the very early Universe, right after the Big Bang, an expansion of the Universe extremely rapid, almost explosive. And that allowed us to understand why the photons of the CMB in different parts of the sky are causally connected. It turns out that they come from the same very tiny region of space time at the beginning of inflation. One important consequence of inflation is the fact that space is flat. So that’s a prediction. As we will see, that prediction can be tested by observation. That’s a very important prediction of the scenario of inflation.

Skip to 15 minutes and 33 seconds Now, in the next sequence, we’ll get a little deeper into that scenario and try to understand what could be the cause of such a very rapid expansion of the Universe at a very early stage.

From horizon to inflation

It is now time to introduce the scenario of cosmic inflation, a period of very fast expansion which took place right after the Big Bang. Theorists identified this stage of the evolution by trying to solve some fundamental issues associated with the causality. This will allow us to identify the important notion of cosmic horizon. (15:52)

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