The turbulence of gravitational waves put into an equation

The recent direct observations of gravitational waves by scientists in the LIGO-Virgo Collaboration suggest new discoveries on how our universe works. A researcher at the Laboratoire de Physique des Plasmas [Plasma Physics Laboratory] has just published a new theoretical model with a colleague which could lift part of the veil on the physics at work in the very early universe.  

Vacuum bubbles in the early universe (unlicensed artist's image)

We are currently experiencing a real revolution in astrophysics with increased direct observations of gravitational waves. This new astronomy promises us many surprising discoveries in the coming years on how our near or distant universe works. But what about the theoretical study of gravitational waves?  

Sébastien Galtier, a Professor at Université Paris-Sud and a researcher at Laboratoire de Physique des Plasmas [Plasma Physics Laboratory] (CNRS / Ecole Polytechnique / UPSud / UPMC / Observatoire de Paris) is studying turbulence phenomena that can be observed in fluids or plasmas from quantum scales (superfluids) up to astrophysical scales.

In an article published recently in the prestigious US journal, Physical Review Letters, which he is the lead author of, he has just revealed some surprising results. Both researchers studied the unstable behaviour of a random ensemble of low-amplitude gravitational waves. Such behaviour can be expected in extreme cases like the environment of black holes or the very early universe: indeed, at around 10-36s GUT (Grand Unified Theory) (1) symmetry breaking is expected, which according to some scenarios, could result in the transition from one phase to another, resulting in the generation of vacuum bubbles (see the diagram); the collisions of these bubbles would be a powerful source of gravitational waves.

Extremely sophisticated mathematical tools

In their studies, the researchers have derived – by rigorous mathematical development – equations for gravitational wave turbulence, as well as their exact solutions. Their calculations are based on Albert Einstein’s general relativity equations which are supposed to be valid beyond Planck time (10-43s). They have demonstrated that an initial forcing of the space-time metric around a kF wave number leads to an excitation in metric fluctuations in wave numbers which are larger and smaller than kF.

In the first instance, the direct energy cascade to the smallest scales is limited by the Planck length under which quantum gravity dominates. In the second instance, the inverse energy cascade is explosive with, in principle, the possibility of exciting fluctuations from kF to k=0 (infinite scale) in a finite time. The mechanism described in the article, however stops at the scale where turbulence becomes strong. In addition, this inverse energy cascade provides an effective mechanism for homogenising the primordial fluctuations in the universe. 

Exciting prospects

Indeed, recent digital studies demonstrate that the space-time metric around black holes is subject to an inverse energy cascade phenomenon which is yet to be understood. Furthermore, Sébastien Galtier and his colleague's studies suggest the possibility of an accelerated expansion mechanism of the early universe by non-linear effects, particularly if (this is not the only condition) the inverse transfer mechanism can be extended to the regime of strong turbulence.  

At a time when many cosmological questions remain unresolved (the origins of dark energy, dark matter or cosmological inflation), non-linear physics – which is highly developed in the field of plasmas – could provide some original and surprising answers. 

(1) : Since the 1970s, several so-called grand unified theories (GUT) have tried to give a unified description of the electromagnetic and strong and weak nuclear forces. However, these theories are very difficult to separate or to confirm experimentally, because there is no accelerator sufficiently powerful enough to test them.

Galtier & Nazarenko, Turbulence of weak gravitational waves in the early Universe, Phys. Rev. Lett. 119, 221101, 2017.