Kinetic and related models with applications in the natural sciences

Turbulence of weak gravitational waves and cosmology

Sebastien Galtier

Universite Paris-Sud


In February 2016, the first direct detection of a gravitational wave (GW) was announced by the LIGO and Virgo laboratories. This GW was produced by merging two black holes into one larger black hole. The difference - about three times the mass of the Sun - was transformed into a GW radiation. GWs are also expected to be produced in the primordial Universe (around the inflation). In this case, the GW amplitudes were probably large enough to consider a nonlinear feedback . In this talk, I will present the GW turbulence theory in which we studied the nonlinear behavior of a random set of weak GWs [1]. This theory is based on the equations of general relativity: we have considered a flat space-time with small perturbations of the metric. While at the linear level we obtain the GWs, at the non-linear level we show the presence of a double cascade of the space-time metric. The direct cascade is limited by the Planck scale below which the equations of general relativity become invalid. The inverse cascade is explosive with the possibility to excite fluctuations from the forcing scale to k=0 in a finite time. The mechanism described stops, however, at the scale where the turbulence becomes strong. I will show numerical simulations to illustrate the inverse cascade mechanism and I will discuss the potential consequences of this turbulence regime for cosmology (inflation, turbulence around black holes). [1] Galtier S. & Nazarenko S.V., Phys. Rev. Lett. 119, 221101, 2017