Late time evolution of the gravitational wave damping in the early Universe

TL;DR

This paper derives an analytical series solution describing how gravitational waves are damped over time in the early Universe due to neutrino streaming, enhancing understanding of early cosmological dynamics.

Contribution

It introduces a new compact formula for convolutions of spherical Bessel functions, enabling an exact series solution for gravitational wave damping.

Findings

Analytical late-time solution for gravitational wave damping.

Series expressed as spherical Bessel functions of even order.

New convolution formula for spherical Bessel functions.

Abstract

An analytical solution for time evolution of the gravitational wave damping in the early Universe due to freely streaming neutrinos is found in the late time regime. The solution is represented by a convergent series of spherical Bessel functions of even order and was possible with the help of a new compact formula for the convolution of spherical Bessel functions of integer order.