Massive Gravity on de Sitter and Unique Candidate for Partially Massless Gravity

TL;DR

This work derives the decoupling limit of massive gravity on de Sitter in arbitrary dimensions by embedding dS into a higher-dimensional Minkowski space to cleanly identify helicity-0 and helicity-1 modes, revealing a decoupling structure similar to the Minkowski case and induction of Galileon-type interactions. It identifies a unique fully non-linear candidate for partially massless gravity—existing within the decoupling limit for a specific parameter set—where the helicity-0 mode decouples, and shows a novel Vainshtein mechanism in the m^2 → 2 H^2 regime unless the PM parameters are exactly realized. The paper also discusses the interplay between PM symmetry, matter couplings, and degrees of freedom counting, arguing that in the PM case the helicity-0 mode can decouple without a Vainshtein mechanism due to a symmetry that fixes the matter coupling (T = 0 in the PM limit). It further analyzes PM gravity in dimensions other than four, noting that while the DL PM structure extends, full non-linear PM behavior may be dimension-dependent and four dimensions exhibit special conformal features. Overall, the work provides a unified DL framework for MG on dS, connects graviton mass bounds to m^2 − 2 H^2, and highlights a unique PM candidate with potential cosmological and symmetry implications.

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\to 2 H^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.