An analytic description of the damping of gravitational waves by free streaming neutrinos

TL;DR

This paper presents an analytic solution to the equation describing how free streaming neutrinos dampen gravitational waves in the early universe, using spherical Bessel functions.

Contribution

It provides a novel analytic solution to the damping equation, expressed as a series of spherical Bessel functions dependent on the wave number.

Findings

Analytic expression for damping of gravitational waves by neutrinos

Series solution involving spherical Bessel functions

Dependence of damping on wave number Q

Abstract

We provide an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe. Our result is expressed as a series of spherical Bessel functions whose coefficients are functions of the reduced wave number $Q$.