On the difficulty of generating gravitational wave turbulence in the early universe

Abstract

A recent article by Galtier and Nazarenko (2017 Phys. Rev. Lett. 119 221101) proposed that weakly nonlinear gravitational waves could result in a turbulent cascade, with energy flowing from high to low frequency modes or vice versa. This is an interesting proposition for early universe cosmology because it could suggest some ‘natural’ initial conditions for the gravitational background. In this paper we use the ADM formalism to show that, given some simple and, arguably, natural assumptions, such initial conditions lead to expansion (or collapse) of the spacetime on a timescale much faster than that of the turbulent cascade, meaning that the cascade is unlikely to have sufficient time to develop under general conditions. We suggest possible ways in which the expansion could be mitigated to give the cascade time to develop.