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