The universe we are in has two enigma-like properties.

First, it is homogeneous on a large scale: when we analyze the cosmic microwave background, in other words its so-called “fossil” radiation which was released more than 13 billion years ago, we realize that its temperature is everywhere the same, in all directions. However, for the temperature of a medium to become uniform, all the parts of this medium must have had time to interact with each other, so that the energy could be distributed equitably. We all know, in fact, that a glass of water placed in a room takes a certain time to reach room temperature. However, calculations show that the period which separated the big bang from the release of the cosmic microwave background radiation, 380,000 years long, is too short for all the regions of the universe to have had time to interact given the fact that the speed of light cannot be exceeded. So how could this radiation have become homogeneous? One could of course postulate that it had this property from the start, but a postulate cannot constitute a true explanation. The homogeneity of the universe therefore has a scent of enigma.

Then, on examination, the universe turns out to be flat as a dab. This does not mean that it is planar, but that the geometry of its spacetime has no curvature. *A priori*, this curvature could be positive, negative, or exactly zero. Now it happens that it is this last situation – the most singular that there is – which has been observed by different measurements: in the universe, two parallels never meet, which means that the metric is globally Euclidean. What a strange coincidence!

## The inflation hypothesis to solve the riddle of the “flatness of the universe”?

Einstein’s equations tell us that the spatial curvature of the universe is determined by the density of matter and energy it contains. But then, how is it that the average density of the universe is exactly that which corresponds to a globally zero curvature? How does it come to be precisely zero rather than any other value? This is called the “riddle of the flatness of the universe”.

In 1981, two cosmologists, Alan Guth and Alexei Starobinsky, advanced (independently of each other) a hypothesis likely to solve these two problems. According to them, the primo-primordial universe would have known a gigantic “inflation”, that is to say a furiously accelerated phase of expansion when its density was extremely high. The figures speak for themselves: the distances would have been multiplied by an enormous factor, of the order of 1050, in a very short time, of the order of 10–32 seconds! This is not what is called a senator’s train… To realize the fulgurance of this process, the gigantism of this growth rate, it suffices to compare it with the following data: during the last ten billion years of the universe, the distances within it have only been multiplied by a factor of 104 (or only 10,000). This is to say if, after a hyper-thunderous start, the expansion of the universe has frankly calmed down. (…)

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