2.7

## Paris Diderot

Skip to 0 minutes and 13 secondsWe have seen in the last sequence that the Universe is in expansion, that because the velocity of light is finite, the further one observed, the earlier in time. And in fact, one is observing the Universe in a slice of spacetime.

Skip to 0 minutes and 33 secondsNow, one of the basic properties of the Universe at large, in its largest distances, is the fact that the Universe is homogeneous. So let me try to explain what I mean by that. We have here a map of the distant galaxies. And you see that if I divide this map into four identical parts, basically I see in the four identical parts, I see the same distribution. So this expresses the fact that the Universe is homogeneous. That means, in particular, that the density of energy, which is defined as the energy divided by the volume, is constant. So it is the same in the four different parts.

Skip to 1 minute and 24 secondsNow, you might think that this definition of homogeneity depends on the observer. For example, from the fact that we are observing from the Earth. Now, the point is that if we take different observers in the Universe of course, the immediate surroundings will be different. We are in the galaxy, other observers might be in a different galaxy. But if they look at the largest scales, the largest dimensions of the Universe they will basically see the same. We will basically measure the same kind of map of distant galaxies as the one I've just shown.

Skip to 2 minutes and 2 secondsAs the Universe expands, the energy density, that is, the energy per unit volume, decreases. In order to understand that, let me return to our model of Universe So this is my inflated balloon with, you see, different galaxies in this Universe And now, let me inflate this Universe Let it expand.

Skip to 2 minutes and 39 secondsSo you see that the average energy per unit volume is decreasing, just because the size of the balloon is increasing. And so, in this way, the energy density is decreasing as the Universe expands. Now, let me get rid of our Universe and turn to another aspect, which is the fact that, again, with expansion, the temperature and the energy is also decreasing. Correspondingly, the temperature of the Universe decreases. This is not surprising, because I remind you that the temperature is understood at a microscopic level as the agitation of molecules. And for example, if I assume that these balloons are molecules, then depending on the energy, agitation, you see, will be increasing or decreasing.

Skip to 3 minutes and 41 secondsNow, because the energy of the Universe is decreasing, the molecular agitation is also decreasing, and so the temperature of the Universe is decreasing. You may understand this phenomenon by looking at this diagram, where you have on the top molecules in a box. So you see that they hit very frequently the wall of a box. Now, the box's size is expanding. And so you see that on the bottom the box has expanded. And so the molecules are hitting the walls of the box less frequently, and so there is less agitation. The temperature has been decreasing.

Skip to 4 minutes and 25 secondsWe will be describing the different epochs of the evolution of the Universe using either energy or temperature. But before I do that, let me tell you which units I'll be using for these quantities. As far as temperature is concerned, I will not be using the traditional Celsius degree. I'll be using the Kelvin. Now, remember that we defined temperature as a molecular agitation.

Skip to 4 minutes and 55 secondsNow, there is a temperature, which corresponds to minus 273 Celsius, which corresponds to no agitation at all. This is called the absolute zero. This corresponds to 0 Kelvin. Now, as you can see on this table, the absolute zero corresponds to minus 273 degrees Celsius. This is 0 Kelvin. Correspondingly, 0 degrees Celsius corresponds to plus 273 Kelvin, and so on. Now, regarding energy units, we will be using particle physics units. So those used in accelerators. We will be using the electronvolt. The electronvolt is the energy of an electron, which is submitted to a voltage of one volt.

Skip to 5 minutes and 53 secondsNow, since we'll be using heavily powers of 10, maybe this is a time just to refresh your memory and discuss precisely these powers of 10. So remember that when I say 10 to a certain number, that means 1 followed by this number of zeros. So 10 to the 3 is 1 followed by three zeros is 1,000. 10 to the 6 is 1 million. 10 to the 9 is 1 followed by nine zeros, 1 billion. For example, in the case of electronvolts, as I was just discussing, then 10 to the 6 electronvolt is what we call the Mega-electronvolt, or MeV. 10 to the 9 electronvolts, so 1 followed by nine zeros electronvolt, is what one calls a Giga-electronvolt, or a GeV.

Skip to 6 minutes and 49 secondsNow, similarly, we can discuss also negative powers of 10. So for example, 10 to the minus 3 is 1 over 10 to the 3, 1 over 1,000. So for example, a millimetre is 10 to the minus 3 metres. 10 to the minus 6 is 1 over 1 followed by six zeros, so one millionth. And 10 to the minus 9 is 1 over 1 followed by nine zeros, one billionth. So for example, a nanometer is 10 to the 9 metres.

Skip to 7 minutes and 31 secondsSo we will describe the different epochs of the evolution of the Universe using energy or temperature. We have seen that this is somewhat equivalent. We could also use the spectral redshift. We have seen that, because of the expansion of the Universe, there is a Doppler shift of the frequencies of light. So that measures distance, but in a way, distance is related with time because of the finiteness of the velocity of light. And of course, we might use time itself in order to describe the different epochs. And so you see on this slide a sort of summary of the evolution of the Universe from the Big Bang until today.

Skip to 8 minutes and 14 secondsAnd you may notice that the most of the events take place between the Big Bang and the first three minutes. And so, in a sense, the time is not a very good variable.

Skip to 8 minutes and 35 secondsIn order to help you understand why time is not such a good variable, or useful one, at least to discuss the very early epochs of evolution, let me take the example of a roller coaster. You certainly have been on a roller coaster. And you may remember that time is sort of flying when you are in the very steep first fall. And then time seems to run more slowly as, little by little, you get to the end of the roller coaster. Of course, this is not physical time. But that shows you that sometimes the evolution is so fast, that one has to use a different measure of time.

Skip to 9 minutes and 20 secondsIn the case of a roller coaster, you could use the height, which is of course much more important in the first fall. In the case of the Universe, instead of talking of the first 10 to the minus 35 seconds, ten to the minus 18 seconds, ten to the minus 3 seconds, we'll be preferring to use the energy or the temperature to describe the different epochs of these very early stages of the Universe.

# An evolving Universe

Because the Universe is expanding, it is dynamical and thus it has a history. How do we follow this history? We review the many parameters that may help to describe this history: time, energy density, temperature, distance, redshift. (9:54)