Cosmological perturbations of self-accelerating universe in nonlinear massive gravity

TL;DR

This paper analyzes cosmological perturbations in a nonlinear massive gravity theory, revealing that scalar and vector modes are non-dynamical or strongly coupled, while tensor modes are modified, affecting gravitational wave propagation.

Contribution

It demonstrates that in nonlinear massive gravity, scalar and vector perturbations are non-dynamical, and the tensor sector exhibits a modified dispersion relation for gravitational waves.

Findings

Scalar and vector perturbations have vanishing kinetic terms.

Tensor perturbations are modified by a time-dependent graviton mass.

Gravitational wave spectrum may be altered in this theory.

Abstract

We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modification of stochastic gravitational wave spectrum.