Dispersion relaxations for zero-helicity gravitational waves in a relativistic expanding medium

Abstract

Presents a study of evolution of helicity-0 waves (density waves) on the FRW cosmological background by using a two-time scale method for solving the perturbed field equation. The kinetic description is adopted by means of the collisionless Liouville equation self-consistently coupled with Einstein's equations. The wave packets obtained are solutions of the shift type. The effects of the expansion of the background (geometrical effects) are contained in these solutions and lead to a power law for the scale factor instead of an exponential law in time. The rate of growth is obtained from dispersion relations which are studied in the case of a cold gravitational plasma. For large wavenumber q the Newtonian dispersion relation is recovered as is the time behaviour of the Newtonian solution, and for vanishing q the behaviour of the relativistic hydrodynamics for the pressureless case is also recovered. It is found that in a relativistic treatment of the cold gravitational plasma, the smaller q becomes the faster the instability grows.