Stability of the Self-accelerating Universe in Massive Gravity

TL;DR

This work analyzes linear perturbations around time-dependent self-accelerating backgrounds in $\\Lambda_3$ massive gravity and shows that scalar perturbation dynamics are frame-dependent via the fiducial metric. When the background yields $A_2=0$, no scalar DOF propagates at linear order due to a gauge-like symmetry; otherwise, a single scalar mode propagates but its Hamiltonian is unbounded from below, indicating instability. The authors explore explicit background solutions across different frames, demonstrating frame-dependent propagation and linking to decoupling-limit results, which partially capture but do not fully constrain the full theory's linear instabilities. They conclude that self-accelerating solutions in this theory are generically unstable to perturbations, challenging their viability for explaining cosmic acceleration. The analysis highlights the subtle interplay between background choice, perturbation dynamics, and the decoupling limit in massive gravity.

Abstract

We study linear perturbations around time dependent spherically symmetric solutions in the Lambda_3 massive gravity theory, which self-accelerate in the vacuum. We find that the dynamics of the scalar perturbations depend on the coordinate choice for the background solutions. For particular choices of coordinates there is a symmetry enhancement, leaving no propagating scalar degrees of freedom at linear order in perturbations. In contrast, any other coordinate choice propagates a single scalar mode. We find that the Hamiltonian of this scalar mode is unbounded from below for all self-accelerating solutions, signalling an instability.