Damping of cosmological tensor modes in Horndeski theories after GW170817

TL;DR

This paper explores how Horndeski theories of gravity modify the damping of cosmological gravitational waves by free-streaming neutrinos, providing new analytic formulas and highlighting differences from general relativity.

Contribution

It derives the Einstein-Boltzmann equation for tensor mode damping in Horndeski theories and shows that modified gravity can cause non-zero damping effects during matter domination.

Findings

Modified gravity introduces non-vanishing damping of tensor modes.

Analytic formulas for damping multipoles in Horndeski theories.

Differences in tensor correlation functions compared to general relativity.

Abstract

This paper investigates the propagation of cosmological gravitational waves interacting with free-streaming neutrinos within the context of Horndeski theories of gravity constrained by the detection of GW170817. We apply the theory of cosmological perturbations to explicitly derive the Einstein-Boltzmann equation for the damped propagation of first-order transverse traceless gravitational waves. In contrast to general relativity, we argue that modified gravity can give rise to non-vanishing free-streaming damping effects during the cosmological matter dominated era. We also provide an analytic formula for the main multipole order with which modified gravity and free-streaming neutrinos damp the variety of tensor correlation functions of the cosmic microwave background.