Non-perturbative Massive de Sitter Solutions

TL;DR

This paper explores non-perturbative solutions in massive gravity on de Sitter space, revealing new vacuum states and challenging perturbative ghost and stability assumptions, with potential cosmological implications.

Contribution

It constructs exact non-perturbative solutions in massive gravity on de Sitter space and reinterprets the Higuchi bound as a non-perturbative critical mass.

Findings

Existence of vacuum solutions with contracting and expanding phases

Identification of a critical mass above which such solutions do not exist

Non-perturbative stability despite perturbative ghost issues

Abstract

We discuss non-perturbative dynamics of massive gravity in de Sitter space via gravitational Higgs mechanism. We argue that enhanced local symmetry and null (ghost) state at (below) the perturbative Higuchi bound are mere artifacts of not only linearization but also assuming the Fierz-Pauli mass term. We point out that, besides de Sitter, there are vacuum solutions where the space asymptotically is de Sitter both in the past and in the future, the space first contracts, this contraction slows down, and then reverses into expansion, so there is an epoch where the space appears to be (nearly) flat, even though the vacuum energy density is non-vanishing. We confirm this by constructing a closed-form exact solution to full non-perturbative equations of motion for a "special" massive de Sitter case. We give a formula for the "critical" mass above which such solutions apparently do not exist. For the Fierz-Pauli mass term this "critical" mass coincides with the perturbative Higuchi bound, and the former serves as the non-perturbative reinterpretation of the latter. We argue that, notwithstanding the perturbative ghost, non-perturbatively there is no "instability". Instead, there are additional vacuum solutions that may have interesting cosmological implications, which we briefly speculate on.