Stability of cosmological solutions in extended quasidilaton massive gravity

TL;DR

This paper investigates the stability of self-accelerating solutions in extended quasidilaton massive gravity with matter, revealing that matter can induce instabilities and that stability depends on specific matter configurations and parameters.

Contribution

It demonstrates that matter can cause instabilities in extended quasidilaton massive gravity and identifies conditions under which solutions remain stable or become unstable.

Findings

Stability is limited for $\\Lambda$CDM expansion history.

No stable solutions for kinetic energy dominated expansion.

Stability depends on matter configuration and parameters.

Abstract

We consider the stability of self-accelerating solutions to extended quasidilaton massive gravity in the presence of matter. By making a second or extended fiducial metric dynamical in this model, matter can cause it to evolve from a Lorentzian to Euclidean signature, triggering a ghost instability. We study this possibility with scalar field matter as it can model a wide range of cosmological expansion histories. For the $\Lambda$CDM expansion history, stability considerations substantially limit the available parameter space while for a kinetic energy dominated expansion, no choice of quasidilaton parameters is stable. More generally these results show that there is no mechanism intrinsic to the theory to forbid such pathologies from developing from stable initial conditions and that stability can only be guaranteed for particular choices for the matter configuration.