Stability of the Early Universe in Bigravity Theory

Understand

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.