The impact of cosmic neutrinos on the gravitational-wave background

TL;DR

The paper addresses the evolution of the cosmological gravitational-wave background at second order in perturbation theory with a focus on the radiation-dominated epoch and the role of cosmic neutrinos. It derives the second-order GW equation in Fourier space with a source term that includes Einstein, neutrino, and photon contributions, and solves the collisionless Boltzmann equation for neutrinos to obtain the tensor part of their anisotropic stress. A key result is the identification of a new neutrino induced source term driven by the high velocity dispersion of collisionless neutrinos, in addition to the known damping from free streaming, and the complete expression requires full angular and momentum integration of the Boltzmann solution. The photon contribution is treated consistently through the second-order photon quadrupole, revealing coupling effects between neutrinos and photons in the TT GW source. Overall, treating neutrinos as a fluid underestimates their impact on the stochastic gravitational-wave background, underscoring the importance of a full kinetic treatment for precise predictions relevant to future GW detectors and CMB polarization probes.

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.