Space-time is not a material medium, yet its dynamics resemble that of fluids. Like them, it could have become turbulent, especially at the time of the Big Bang, when it was traversed by gravitational waves. Numerical simulations support the existence of this phenomenon which seems to provide an alternative to the standard inflation scenario in primordial cosmology.

Hydrodynamics is a science whose beginnings go back a long way and this is not surprising given that the flow of water or the behavior of liquids have always fascinated man and that the first engineers, before Archimedes, sought to control the transport of water. The designs that Leonardo DeVinci left us in several of these notebooks are an excellent illustration of this fascination and these concerns.

Regret Michel Serres had assumed a link between the contemplation of the swirling behavior of water and the birth of Greek atomic physics described by the famous poem of the epicurean philosopher Lucretia.

But it was not until the works ofEuler and Bernoulli so that equations Powerful mathematics are beginning to account for these phenomena. Today, even if we think that Navier-Stokes equations, joined to the principles of thermodynamics and to the equations ofelectromagnetism, describe almost all the phenomena of fluid flow, there are still mysteries to be solved in hydrodynamics.

There is one that has greatly preoccupied the physicists and engineers of the XX^{e} century (describe the behavior of the oceans,atmosphere and the flow ofair around a plane or a car need *in fine* understanding).

It is that of the turbulence (see on this subject Classes of Nobel Prize in Physics Kip Thorne).

So much so that physicists of the caliber of Feynman and Pram tackled it and that Heisenberg himself spent his thesis on this subject under the direction of Sommerfeld before being illustrated by his discoveries in physical quantum.

## The quantum and classical turbulence of Big Bang space-time

Today, as Futura explained in the previous article below, the physics of turbulence inspires those who seek to understand the foam of space-time mentioned by Jean-Pierre Luminet in one of his previous books. It now seems that even the gravitational waves may exhibit behavior which is analogous to that of fluid turbulence such as physicist Sébastien Galtier shows this more and more clearly with colleagues.

With Jason Laurie and Sergey Nazarenko he published in 2020 an article where it is suggested that a turbulent space-time during the big Bang with some mini holes primordial blacks colliding and emitting gravitational waves feeding this turbulence could have given rise to a phenomenon similar to that of inflation generally postulated as resulting from the effect of a scalar field, theinflaton, analogous to the field of boson of Brout-Englert-Higgs. The first results show that this hypothesis seems compatible with analyzes of the data from the fossil radiation of the Planck mission.

This year, Sébastien Galtier and Sergey Nazarenko published another job in which they confirm by numerical simulations what their analytical calculations had shown in 2017 and which Futura talked about in the previous article below. It is the first time that this kind of simulation shows that a turbulent behavior of space-time can arise with gravitational waves, initially weak then which then become strong. This is one more motivation to further explore the alternative inflation model proposed in 2020 and which is based on these phenomena.

Sébastien Galtier exhibiting his work on the turbulence of space-time. 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”. © Institute of Astrophysics of Paris

What you must remember

- For more than 60 years, physicists have noted analogies between the physics of fluids and those of space-time suggesting that it can become turbulent in certain situations, for example due to quantum gravity.
- This turbulence could also appear when gravitational waves are interacting, for example during the Big Bang, when the forces have separated.

## Gravitational waves would have made the Big Bang space-time turbulent

*Article by Laurent Sacco published on 12/27/2017*

**Space-time is not a material medium but, nevertheless, its dynamics resemble that of fluids. Like them, it could therefore become turbulent, at the time of the Big Bang or near some black holes, especially when it is traversed by gravitational waves.**

The equations of general relativity are non linear, just like those of fluid mechanics, so that it is often difficult to extract predictions. The pitfall can be overcome with the help ofcomputers but they have their limits.

In fact, the behavior of space-time and that of a fluid have many points in common. It is therefore possible to draw some inspiration from the physics of fluids to approach the physics of curved space-times. This is what the great physicist understood in the 1950s and 1960s John Wheeler. In particular, he had advanced arguments suggesting that space-time could behave like a turbulent fluid with a structure in foam on a very small scale, that of Planck, where the distances are of the order of 10^{-35} cm, or less, and times shorter than 10^{-43} s, time and space scales that are found so close to the hypothetical time zero of the Big Bang. Quantum fluctuations in space-time would change its topology, with black holes and microscopic virtual wormholes constantly appearing and disappearing.

A conference on turbulence. © Mission 2000 in France, UTLS

## A turbulent cascade of gravitational waves

Two researchers from the Plasma Physics Laboratory (CNRS, Ecole Polytechnique, Paris-Sud University, UPMC, Paris Observatory) and the University of Warwick took Wheeler’s ideas a step further. According to their hypothesis, other aspects of fluid turbulence may appear, as they explain in an article published in the journal *Physical Review Letters *and available on arXiv.

This work is interesting in more than one way, in particular by its possible connections with the fluid-gravity correspondence which points its nose for some time in the physics of black holes. In this case, the researchers found a new manifestation of the equivalent of the turbulent waterfall in fluid physics, a form of transfer ofenergy between swirls large sizes, possessing a large kinetic energy, and smaller ones that can absorb and dissipate this energy. This phenomenon was the subject of significant work almost a century ago, first by the British mathematician Lewis Richardson in the 1920s and then by his Russian colleague, the mythical Andrei Kolmogorov, in the 1940s.

In the present case, energy transfers associated with the turbulence of space-time would take place thanks to non-linear couplings between gravitational waves of low amplitudes. These waves could for example have been generated by phase transitions in the primordial quantum fields when the forces have disunited, first within the framework of grand unification theories (which remain hypothetical) and at least during the breaking of symmetry of the electroweak force.

According to the researchers, this turbulent cascade phenomenon could have contributed to homogenize the primordial fluctuations of space-time which could be very chaotic at the time of the Big Bang. The question is of importance for work on the fossil radiation and on the abundance of primordial black holes, which could be fossils from the very first moments of the observable cosmos.

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