Massive gravity on de Sitter and unique candidate for partially massless gravity

Abstract

Abstract. We derive the decoupling limit of Massive Gravity on de Sitter in an arbitrary number of space-time dimensions d. By embedding d-dimensional de Sitter into d + 1-dimensional Minkowski, we extract the physical helicity-1 and helicity-0 polarizations of the graviton. The resulting decoupling theory is similar to that obtained around Minkowski. We take great care at exploring the partially massless limit and define the unique fully non-linear candidate theory that is free of the helicity-0 mode in the decoupling limit, and which therefore propagates only four degrees of freedom in four dimensions. In the latter situation, we show that a new Vainshtein mechanism is at work in the limit m 2 → 2H 2 which decouples the helicity-0 mode when the parameters are different from that of partially massless gravity. As a result, there is no discontinuity between massive gravity and its partially massless limit, just in the same way as there is no discontinuity in the massless limit of massive gravity. The usual bounds on the graviton mass could therefore equivalently well be interpreted as bounds on m 2 − 2H 2 . When dealing with the exact partially massless parameters, on the other hand, the symmetry at m 2 = 2H 2 imposes a specific constraint on matter. As a result the helicity-0 mode decouples without even the need of any Vainshtein mechanism.

On partially massless bimetric gravity

“…To compare results, we need to take a massive gravity limit of (4.6) by setting m f = ∞ (or α = ∞) keeping β 2 fixed. This gives β 0 = 0 and β 4 = α 2 β ′ 4 for a finite β ′ 4 , agreeing with the parameters for which [23] finds an extra PM symmetry in the decoupling limit 3 , although, in general the two formalisms lead to different predictions, as described below.…”

“…In [23], the authors identify a specific nonlinear massive gravity which, in a decoupling limit adapted to dS spacetimes, shows a non-linear PM symmetry. To compare results, we need to take a massive gravity limit of (4.6) by setting m f = ∞ (or α = ∞) keeping β 2 fixed.…”

“…The fluctuations around these backgrounds do not have the Fierz-Pauli form. However, for the parameter values specified by (4.6), and in the absence of sources, the equation that determines Υ = Y /a 3 Comparison with the theory found in [23] requires some care. The massive gravity action presented there contains the original dRGT potential which is constructed with α1 = 0 so that the gµν = fµν solutions have zero cosmological constant.…”

“…Using this action one reads off β1 = β3 = 0, β2 = − 1 2 and β0 = 3 2 = 0 (for example, using the relations in appendix B of [36]). However, to find the PM symmetry, [23] considers perturbations around gµν = fµν backgrounds with a de Sitter fµν . The correct action corresponding to this must have α1 = 0 such that β0 = 0, consistent with the massive gravity limit of the theory found here.…”

“…In the context of massive gravity, this question was recently investigated in [23], in a decoupling limit specifically developed for the de Sitter space. The authors discover the parameter values for which the Stückelberg field that captures the dynamics of the helicity-zero mode of the graviton is removed to all orders in the decoupling limit.…”