Derivative couplings in massive bigravity

TL;DR

This paper investigates cosmological perturbations in massive bigravity with non-minimal derivative couplings, focusing on a specific Horndeski scalar-tensor interaction, and confirms the propagation of physical degrees of freedom without ghosts.

Contribution

It introduces a consistent framework for derivative couplings in massive bigravity, analyzing their effects on cosmological perturbations and degrees of freedom.

Findings

Only four tensor, two vector, and two scalar degrees of freedom propagate.

The Boulware-Deser ghost can be integrated out.

The model remains viable with a single kinetic term.

Abstract

In this work we study the cosmological perturbations in massive bigravity in the presence of non-minimal derivative couplings. For this purpose we consider a specific subclass of Horndeski scalar-tensor interactions that live on the unique composite effective metric. For the viability of the model both metrics have to be dynamical. Nevertheless, the number of allowed kinetic terms is crucial. We adapt to the restriction of having one single kinetic term. After deriving the full set of equations of motion for flat Friedmann-Lemaitre-Robertson-Walker background, we study linear perturbations on top of it. We show explicitly that only four tensor, two vector and two scalar degrees of freedom propagate, one of which being the Horndeski scalar, while the Boulware-Deser ghost can be integrated out.