  A recent article by Galtier and Nazarenko [1] 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.
