Stability of the Self-accelerating Universe in Massive Gravity
Nima Khosravi (AIMS, Cape Town), Gustavo Niz (ICG, Portsmouth and, Guanajuato U.), Kazuya Koyama (ICG, Portsmouth), Gianmassimo Tasinato (ICG,, Portsmouth)
TL;DR
This paper investigates the stability of self-accelerating solutions in Lambda_3 massive gravity, revealing coordinate-dependent scalar perturbation dynamics and an inherent instability due to an unbounded Hamiltonian.
Contribution
It demonstrates that scalar perturbations in self-accelerating solutions depend on coordinate choice and identifies an instability through Hamiltonian analysis.
Findings
Scalar perturbations depend on coordinate choice.
Certain coordinates exhibit symmetry enhancement with no propagating scalars.
All solutions show an instability due to an unbounded Hamiltonian.
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.
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