In 1965, the Nobel Prize in Physicspublished a demonstrating that the of the theory of D’ implied that the gravitational force of a sufficiently massive star had necessarily to lead to a singularity of the surrounded by a and therefore inside a . Before him, this occurrence was thought to be an artifact of idealized solutions of Einstein’s equations. In 1969 he published with . One could indeed consider that many solutions of Einstein’s equations describing a in expansion were more or less equivalent, by reversing the direction of the flow of time, to that describing a star in gravitational collapse.
Under very general conditions, therefore, Einstein’s equations implied that space and time had a beginning, a beginning during which the density and temperature of its contents, as well as the curvature of space-time, tended towards infinity as one approached asymptotically an instant zero.
Nobel Prize winner Roger Penrose explaining his work in 2021. To obtain 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”. Choose “French”. © Tencent WE Summit
But already, in the minds of Hawking and his colleagues at that time, it must have been just an artefact of a non-quantum treatment of spacetime and perhaps also simply of Einstein’s equations. It is indeed possible to consider different equations governing a curved space-time and when a volume of theobservable was much smaller at the beginning of the expansion, its contents had to behave like a quantum. Now, we know well that the laws of precisely ensure a finite size to an atom by suppressing any collapse of its layers of on its core. In fact, by the end of the 1960s, .
The works ofquantum which were to follow, for example those of and more recently from were going to revisit questions already tackled in the 1920s and 1930s by Alexandre Friedmann, 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 consider that nature had perhaps “chosen” to manifest itself in the form of a cyclic cosmology without beginning or end, oscillating perpetually between aand one – to use a terminology which will only appear after the Second World War and which is now well known to the general public.
The thermodynamics of the Big Bang
But, as early as the 1930s, the American Richard Tolman, who had begun his career inphysics before becoming a world authority in whether classical or quantum, and in had laid the foundations for reflections which would show that there was potentially a problem with the thermodynamics of relativistic cyclic cosmology. A problem that was to get worse after the discovery of the in 1965.
Indeed, Tolman had thus succeeded in transposing within the framework of curved space-times of relativistic cosmology the laws of thermodynamics and in particular those closely related toone of the most fundamental state functions of thermodynamics. It finally resulted thereafter that at each new phase of a cyclic cosmology, the entropy of its content in and radiation had to grow (it can be estimated with the measurement of the ratio of the number of photons to the number of in the observable cosmos as well as with its black hole content). It was difficult to reconcile with the observation that the entropy measured today is not only finite but very far from being maximum, 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 at the end of his famous book .
The question of what happens with entropy for cyclic universes and what Tolman thought about it is more complex than just explained, but we continue to reflect on the difficulties it raises. A few years ago, the famous cosmologist andtheorist Paul Steinhardt revisited these questions with his colleague .
The two researchers have published articles oninvolving a scalar field, and equations governing an interaction between this field and the expansion of the observable cosmos. This scalar field, sometimes called can be used to describe the nature of and it allows the acceleration of the expansion of the cosmos to change into 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 ofand, shortly before reaching it, at a black holes formed during the phase. This fusion could make the rebound impossible and above all, the passage through a quantum phase should cause the next phase to begin with a very high state of the entropy of the observable cosmos, which is not observed.
Anna Ijjas explains her work with Paul J. Steinhardt on a cyclical cosmology. To obtain 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”. Choose “French”. © Dr. Brian Keating
A cyclic cosmology without quantum bounce
then showed that with the scalar field model they introduced, the contraction stops well before reaching the Planck density and the cosmos rebounds. But it rebounds with a larger expansion factor than during the previous phase, whereas this factor oscillates periodically, resuming its values in the previous models of cyclic cosmology.
In doing so, the extra entropy produced by the previous phase is somehow diluted and pushed outside of what is called the. For an observer below this horizon, there is no longer a continual increase at 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 cycles in the past.
But two other cosmologists from the University of Buffalo in the United States,and Nina K. Stein, have just thrown a stone into the pond. According to them, as they explain in an open-access publication on even the cyclic universe of Ijjas and Steinhardt must have a beginning in time with an initial singularity.
The two researchers took up the reasoning already put forward several years ago byinspired by those of Penrose and Hawking, who showed that even the famous theory of inflation which was also supposed to make it possible to avoid an initial singularity and to avoid asking questions about the concept of the beginning of the Universe, could not in fact do without these two ideas.
Technically, it is the demonstration of a theorem relating to what is called the completeness of the geodesics of a space-time. These geodesics are the trajectories that light rays and particles of matter must take under the sole effect of the curvature of space-time. William Kinney and Nina K. Stein, as well as Arvind Borde, Alan H. Guth and Alexander Vilenkin came to the conclusion that geodesics in the cosmology of Ijjas and Steinhardt could not be parametrized by a variable which could reach infinity, which which showed 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 come up with bouncing universes to make the Universe infinite in the past, but what we’re showing is that one of the newer types of those models doesn’t work. In this new type of model, which deals with entropy issues, even though the universe has cycles, it must still have a beginning. »
While specifying that: Unfortunately, it’s been known for almost 100 years that these cyclic patterns don’t work because disorder, or entropy, builds up in the Universe over time, so each cycle is different from the last. It’s not really cyclical. A 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, long story short, we showed that by solving the entropy problem, you create a situation where the Universe had to have a beginning. Our proof shows in general that any cyclic pattern that removes entropy by expansion must have a beginning. »
Kinney concedes, however: Our proof does not apply to a. We are working on this issue. »