Gravitational waves in a flat radiation-matter universe including anisotropic stress

TL;DR

This paper derives accurate analytical solutions for gravitational waves in a flat universe with radiation, matter, and neutrino anisotropic stress, applicable to primordial and sub-horizon waves, improving previous approximations.

Contribution

It provides novel analytical solutions for gravitational waves in a universe with multiple fluids and anisotropic stress, valid before and after horizon crossing.

Findings

Analytical solutions are accurate within 1% for relevant wave-numbers.

Solutions apply to both primordial and sub-horizon gravitational waves.

Improves upon previous analytical approximations in the literature.

Abstract

We present novel analytical solutions for linear-order gravitational waves or tensor perturbations in a flat Friedmann-Robertson-Walker universe containing two perfect fluids, radiation and pressureless dust, and allowing for neutrino anisotropic stress. One of the results is applicable to any sub-horizon gravitational wave in such a universe. Another result is applicable to gravitational waves of primordial origin, for example produced during inflation, and works both before and after they cross the horizon. These results improve on analytical approximations previously set out in the literature. Comparison with numerical solutions shows that both these approximations are accurate to within $1\%$, or better, for a wide range of wave-numbers relevant for cosmology.