Bumblebee Gravity - Lessons from Perturbation Theory

Abstract: These proceedings summarize some recent efforts in understanding a class of vector-tensor theories known as {\it bumblebee} models, which spontaneously break local Lorentz and diffeomorphism invariance. Using cosmological perturbation theory on an exact dS background, we find that for non-minimal coupling to gravity, the theory contains a ghost mode unless a degeneracy condition is imposed, after which the model becomes a subset of generalized Proca theory. We go further to show that scalar perturbations become strongly coupled in the minimal-coupling limit, which shows the necessity of the non-minimal coupling. Moreover, we find a constraint on the bumblebee field from the speed of tensor modes on the order of $10^{-15}$.