Gravitational wave propagation in bigravity in the late universe

TL;DR

This paper analytically investigates gravitational wave propagation in ghost-free bimetric gravity during late-time de Sitter expansion, deriving exact solutions, regimes, and observational bounds from GW170817.

Contribution

It provides exact solutions and a comprehensive analysis of gravitational wave modes in bimetric gravity, including new observational bounds from GW data.

Findings

Exact solutions for massless and massive graviton modes in late-time de Sitter

Identification of regimes based on the propagation properties of the massive graviton

Derived a new observational bound for bimetric gravity using GW170817

Abstract

We carry out a detailed analytical investigation of the propagation of gravitational waves in ghost-free bimetric gravity in a late-time de Sitter epoch. In this regime, the dynamical equations for the massless and massive graviton modes can be decoupled and solved exactly. We provide uniform approximations for the modes in terms of elementary functions, which are valid on all scales and for all viable mass windows. We identify different dynamical regimes for the system, depending on the propagation properties of the massive graviton, and whether the massless and massive components of the signal can be temporally resolved or not. In each regime, we compute the gravitational-wave luminosity distance as a function of redshift and study the propagation of wave packets. This allows for the derivation of a new observational bound for the ghost-free bimetric theory using the event GW170817. Further, by an explicit computation, we show that the massless and massive components of the signal retain their coherence also in the regime where they can be temporally resolved, even when couplings to incoherent matter degrees of freedom are included.