The impact of cosmic neutrinos on the gravitational-wave background

TL;DR

This paper derives the evolution equation for the cosmological gravitational-wave background considering cosmic neutrinos, revealing a new neutrino-induced source term that influences gravitational wave damping during radiation dominance.

Contribution

It introduces a novel source term from neutrino anisotropic stress in the second-order gravitational wave evolution equation, accounting for neutrino velocity dispersion effects.

Findings

Standard neutrino damping effect confirmed.

New neutrino source term identified and characterized.

Implications for gravitational wave predictions during radiation era.

Abstract

We obtain the equation governing the evolution of the cosmological gravitational-wave background, accounting for the presence of cosmic neutrinos, up to second order in perturbation theory. In particular, we focus on the epoch during radiation dominance, after neutrino decoupling, when neutrinos yield a relevant contribution to the total energy density and behave as collisionless ultra-relativistic particles. Besides recovering the standard damping effect due to neutrinos, a new source term for gravitational waves is shown to arise from the neutrino anisotropic stress tensor. The importance of such a source term, so far completely disregarded in the literature, is related to the high velocity dispersion of neutrinos in the considered epoch; its computation requires solving the full second-order Boltzmann equation for collisionless neutrinos.