Cosmological Perturbations in Extended Massive Gravity

TL;DR

This paper investigates the stability of cosmological perturbations in extended massive gravity theories, finding that kinetic terms are generally non-vanishing and that certain self-accelerating solutions are unstable to scalar perturbations.

Contribution

It analyzes the stability of self-accelerating solutions in quasi-dilaton and mass-varying massive gravity theories, revealing conditions for stability and common instabilities.

Findings

Kinetic terms are generally non-zero in extended theories.

Self-accelerating solutions in quasi-dilaton theory are unstable to short-wavelength scalar perturbations.

Constraints on parameters ensure correct sign of kinetic terms.

Abstract

We study cosmological perturbations around self-accelerating solutions to two extensions of nonlinear massive gravity: the quasi-dilaton theory and the mass-varying theory. We examine stability of the cosmological solutions, and the extent to which the vanishing of the kinetic terms for scalar and vector perturbations of self-accelerating solutions in massive gravity is generic when the theory is extended. We find that these kinetic terms are in general non-vanishing in both extensions, though there are constraints on the parameters and background evolution from demanding that they have the correct sign. In particular, the self-accelerating solutions of the quasi-dilaton theory are always unstable to scalar perturbations with wavelength shorter than the Hubble length.