Stability of the Early Universe in Bigravity Theory

TL;DR

This paper demonstrates that nonlinear effects in ghost-free bigravity can stabilize early universe cosmology, resolving linear instabilities and establishing a viable massless limit consistent with general relativity.

Contribution

It shows that nonlinear scalar graviton effects can eliminate linear instabilities, enabling a healthy massless limit in bigravity cosmology.

Findings

Nonlinearities resolve Higuchi-type ghost and gradient instabilities.

Early universe behavior matches general relativity.

Bigravity remains viable with small graviton mass.

Abstract

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lema$\hat{\i}$tre-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-$0$ mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the St\"uckelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter.