Higuchi Ghosts and Gradient Instabilities in Bimetric Gravity

TL;DR

This paper investigates the conditions under which bimetric gravity models are free of ghost and gradient instabilities, focusing on cosmological solutions and the implications for dark energy and exotic evolutions.

Contribution

It derives conditions for avoiding Higuchi ghosts and gradient instabilities in bimetric gravity, analyzing their implications for cosmological solutions including bouncing universes.

Findings

The ratio of scale factors must increase over time in expanding universes.

Ghost-free conditions imply a phantom dark energy component.

Analysis of stability conditions for exotic cosmological evolutions.

Abstract

Bimetric gravity theories allow for many different types of cosmological solutions, but not all of them are theoretically allowed. In this work we discuss the conditions to satisfy the Higuchi bound and to avoid gradient instabilities in the scalar sector at the linear level. We find that in expanding universes the ratio of the scale factors of the reference and observable metric has to increase at all times. This automatically implies a ghost-free helicity-2 and helicity-0 sector and enforces a phantom dark energy. Furthermore, the condition for the absence of gradient instabilities in the scalar sector will be analyzed. Finally, we discuss whether cosmological solutions can exist, including exotic evolutions like bouncing cosmologies, in which both the Higuchi ghost and scalar instabilities are absent at all times.