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 con- traction 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.
Highlights
Introduction and SummaryThe currently observed accelerated expansion of the Universe [1, 2] is one of the motivations for considering large-scale modifications of gravity
While – barring unbroken supersymmetry – the cosmological constant is not protected, quantum corrections to the graviton mass appear to be suppressed by the graviton mass itself [3]
Generically a ghost reappears beyond the linearized level even for the Fierz-Pauli mass term [5] and, once again, perturbatively, to avoid the reappearance of a ghost beyond the linearized level one attempts tuning the mass term to a special form [3]
Summary
The currently observed accelerated expansion of the Universe [1, 2] is one of the motivations for considering large-scale modifications of gravity. It has a rich structure of apparently well-behaved (non-static) vacuum solutions.5 Motivated by these results and by the observation of [12], in this note we discuss non-perturbative dynamics of massive gravity in de Sitter space via gravitational Higgs mechanism. As was argued in [8], non-perturbatively there is no enhanced symmetry or null state for any value of the graviton mass and these are merely artifacts of linearization as is the perturbative ghost. Despite the fact that perturbatively there is a fake ghost, non-perturbatively the theory does not appear to be “sick” or inconsistent It has a rich structure of (possibly interesting) vacuum solutions.
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