Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations

TL;DR

This paper investigates how second-order anisotropic stresses of photons and neutrinos influence the evolution and spectrum of gravitational waves induced by cosmological density perturbations, revealing significant amplification or suppression effects on small scales.

Contribution

It provides a full Einstein-Boltzmann treatment of anisotropic stresses' effects on second-order induced gravitational waves, a novel analysis not previously explored.

Findings

Photon anisotropic stress amplifies GW amplitude by about 150%.

Neutrino anisotropic stress suppresses GW amplitude by about 30%.

Effects are significant on small scales with wavenumber k > 1.0 h/Mpc.

Abstract

Gravitational waves (GWs) are inevitably induced at second-order in cosmological perturbations through non-linear couplings with first order scalar perturbations, whose existence is well established by recent cosmological observations. So far, the evolution and the spectrum of the secondary induced GWs have been derived by taking into account the sources of GWs only from the product of first order scalar perturbations. Here we newly investigate the effects of purely second-order anisotropic stresses of photons and neutrinos on the evolution of GWs, which have been omitted in the literature. We present a full treatment of the Einstein-Boltzmann system to calculate the spectrum of GWs with anisotropic stress based on the formalism of the cosmological perturbation theory. We find that photon anisotropic stress amplifies the amplitude of GWs by about $150 %$ whereas neutrino anisotropic stress suppress that of GWs by about $30 %$ on small scales $k\gtrsim 1.0 h{\rm Mpc}^{-1}$ compared to the case without anisotropic stress. The second order anisotropic stress does not affect GWs with wavenumbers $k\lesssim 1.0 h{\rm Mpc}^{-1}$. The result is in marked contrast with the case at linear order, where the effect of anisotropic stress is damping in amplitude of GWs.