General Massive Spin-2 on de Sitter Background

We study linearised massive gravity on the de Sitter background. With a smallenough graviton mass this may have had relevance to inflation, or the present-day cosmic acceleration. Higuchi has shown that this theory has a ghost as long as the dS curvature exceeds the graviton mass, 2H2 > m2; this would entail rapid instabilities. In this work we extend the model and observe that the helicity-0 mode which is a ghost, can be turnd into a positive energy state via kinetic mixing with the conformal mode. The latter gets restricted here by the requirement that the Bianchi identities be satisfied. This eliminates the ghost from the linearized theory. However, the spectrum still contains scalar tachyonic instabilities with the time scale ∼ 1/H. This would have been problematic for the early univesre, however, may be acceptable for the present-day accelerated expansion as the tachyon instability would take the age of the universe to develop.