Mass eigenstates in bimetric theory with matter coupling

TL;DR

This paper investigates a ghost-free bimetric gravity theory with a novel matter coupling, deriving conditions under which the metrics are proportional and analyzing the behavior of perturbations, revealing that only the massless mode interacts with matter.

Contribution

It introduces a new matter coupling in bimetric theory, derives solutions with proportional metrics, and analyzes perturbations showing only the massless mode couples to matter.

Findings

Proportional metrics solve the equations under a fixed parameter.

The effective metric obeys Einstein's equations with matter.

Only the massless spin-2 mode interacts with matter.

Abstract

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a matter source. Around these backgrounds we derive the quadratic action for perturbations, diagonalized into a massive and a massless spin-2 fluctuation. We find that only the massless spin-2 mode interacts with matter; a result which is independent of the remaining parameters of the theory.