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[EN VIDÉO] Interview: what do we really know before the Big Bang? The Big Bang is a singularity that is often described as embodying the origin of the universe, but it is possible that it is only one episode of its existence. Futura-Sciences went to meet Etienne Klein, physicist, to find out if something could have preceded him.

In 1965 he received the Nobel Prize for physical Roger Penrose published a theorem shows that equations of the theory of general relativity ofEinstein implied thatcollapse the gravity of a star sufficiently massive must necessarily lead to a singularity ofspace time surrounded by a event horizon and therefore inside one black hole. Before him, this occurrence was thought to be an artifact of idealized solutions of Einstein’s equations. In 1969 he published with Stephen Hawking an improved version of a theorem produced by the latter, who had applied Penrose’s mathematical methods and ideas of relativistic cosmology to demonstrate the occurrence of the same phenomenon with the Big Bang. One could actually consider that many solutions of Einstein’s equations that describe a Universe in expansion were more or less equivalent, by reversing the direction of the flow of time, to what describes a star in gravitational collapse.

In very general terms, Einstein’s equations therefore implied that space and time had a beginning, a beginning where the density and temperature of its contents, as well as the curvature of spacetime, tended toward infinity as one asymptotically approached an instantaneous zero.

Nobel laureate Roger Penrose explains his work in 2021. For a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles should then appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Translate automatically”. Select “French”. © Tencent WE Summit

But already, in the minds of Hawking and his colleagues at the time, it must have been only an artifact of a non-quantum treatment of spacetime and perhaps also simply of Einstein’s equations. Indeed, it is possible to consider various equations governing a curved spacetime, and when one volume from cosmos observable was much smaller at the beginning of the extension, its content had to behave like one atom quantum. Now we know very well that the laws of Quantum mechanics precisely ensure a finite size to an atom by suppressing any collapse of its layerselectrons at its core. In fact, in the late 1960s, Bryce DeWitt had laid the foundation for a quantum theory of gravitation applicable in cosmology.

The works of cosmology quantum which should follow, for example those of Stephen Hawking and more recently from Carlo Rovelliwould revisit questions already addressed in the 1920s and 1930s by Alexandre Friedmann, Georges Lemaitre and Richard Tolman for the most part.

In the hands of these men, it had become clear that Einstein’s equations contained patterns of universes in which the expansion of space eventually slowed before reversing, returning its contents to infinite density. A new phase of expansion could then begin, and one could therefore think that nature had perhaps “chosen” to manifest itself in the form of a cyclical cosmology without beginning or end, constantly oscillating between a big bang and one Big crunch – to use a terminology which only comes after the Second World War and which is now well known to the general public.

## Big Bang Thermodynamics

But already in the 1930s, the American Richard Tolman, who had started his career in chemistry physics before becoming a world authority on it statistical mechanicswhether classical or quantum, and i relativityhad laid the groundwork for reflections which would show that there was potentially a problem with thermodynamics relativistic cyclic cosmology. A problem that was to get worse after the discovery of cosmic radiation in 1965.

In fact, Tolman had thus succeeded in transposing the laws of thermodynamics within the framework of relativistic cosmology’s curved spacetimes and especially those closely related toentropy, one of the most fundamental state functions of thermodynamics. It finally resulted then that at each new phase of a cyclic cosmology, the entropy of its content i fabric and radiation should grow (it can be estimated by measuring the ratio of the number of photons The number of baryons in the observable cosmos as well as with its black hole content). This was difficult to reconcile with the observation that the entropy measured today is not only finite but very far from maximal if one believes that there are both an infinite number of cycles in the past and in the future , as explained by the Nobel Prize Steven Weinberg at the end of his famous book *The first three minutes of the universe*.

The question of what happens to entropy for cyclic universes, and what Tolman thought about it, is more complex than simply explained, but we continue to reflect on the difficulties it raises. A few years ago, the famous cosmologist and physicist theorist Paul Steinhardt echoed these questions with his colleague Anna Ijjas.

The two researchers have published articles on *arXiv* involves a scalar field, like the Higgs boson, and equations governing an interaction between this field and the expansion of the observable cosmos. This scalar field, sometimes called quintessencecan be used to describe the nature of dark energy and it allows the acceleration of the expansion of the cosmos to change to deceleration with contraction.

In itself this is not new, but in the similar scenarios studied so far followed by a rebound phase, a* Big Bounce* as we say in English, the contraction phase led to the density of Plank and shortly before reaching it, at fusion black holes formed during the phase. This merger could make rebound impossible, and above all, the passage through one quantum phase would cause the next phase to begin with a very high state of entropy in the observable cosmos, which is not observed.

Anna Ijjas explains her work with Paul J. Steinhardt on a cyclical cosmology. For a fairly accurate French translation, click on the white rectangle at the bottom right. The English subtitles should then appear. Then click on the nut to the right of the rectangle, then on “Subtitles” and finally on “Translate automatically”. Select “French”. © Dr. Brian Keating

## A cyclic cosmology without quantum bounce

Anna Ijjas and Paul J. Steinhardt then showed that with the scalar field model they introduced, the contraction stops well before it reaches the Planck density and the cosmos rebounds. But it returns with a larger expansion factor than in the previous phase, whereas this factor fluctuates periodically and resumes its values in the previous models of cyclic cosmology.

Thereby the extra entropy produced by the previous phase is somehow diluted and pushed outside what is calledcosmological horizon. For an observer below this horizon, there is no longer a continuous increase in each phase of the expansion of the observable cosmos, and there is no longer a contradiction between the measured entropy and an already infinitely old universe with an infinite number of cycles in the past.

But two other cosmologists from the University of Buffalo in the US, William Kinney and Nina K. Stein, just threw a rock into the pond. According to them, as they explain in an open-access publication on *arXiv*even Ijja’s and Steinhardt’s cyclical universe must have a beginning in time with an initial singularity.

The two researchers took up the reasoning that had already been put forward several years ago Arvind Borde, Alan H. Guth and Alexander Vilenkininspired by Penrose and Hawkings, who showed that even the famous theory of inflation, which should also make it possible to avoid an initial singularity and to avoid questioning the concept of the beginning of the universe, could not actually do without these two ideas.

Technically, it is the demonstration of a theorem concerning what is called the completeness of the geodesic in a space-time. These geodesics are the paths that light rays and particles of matter must take under the sole effect of the curvature of spacetime. William Kinney and Nina K. Stein, as well as Arvind Borde, Alan H. Guth, and Alexander Vilenkin came to the conclusion that geodesics in Ijjas and Steinhardt’s cosmology could not be parametrized by a variable that could reach infinity, as shown in the jargon of differential geometry , that these geodesics are incomplete in the past.

This is why, in a press release from the University of Buffalo, Kinney explains that: *People have previously come up with bouncing universes to make the universe infinite, but what we show is that one of the newer types of these models doesn’t work. In this new type of model, which deals with entropy issues, the universe must still have a beginning, even though the universe has cycles.* »

While stating that: *Unfortunately, it has been known for almost 100 years that these cyclical patterns do not work because disorder or entropy builds up in the universe over time so that each cycle is different from the last. It’s not really cyclical. A more recent cyclical model circumvents this problem of entropy accumulation by proposing that the universe expands with each cycle, diluting entropy. You stretch everything to get rid of cosmic structures such as black holes, which return the universe to its original homogeneous state before another bounce begins.*

*But in short, we showed that by solving the entropy problem, you create a situation where the universe had to have a beginning. Our proof generally shows that any cyclic pattern that removes entropy by expansion must have a beginning.* »

However, Kinney admits: *Our proof does not apply to one cyclical model proposed by Roger Penrose in which the universe expands infinitely with each cycle. We are working on this issue.* »

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