Massive Gravity on Cosmological Backgrounds
Abstract: I will discuss generally covariant theories of non-linear
massive gravity admitting isotropic background solutions. The question
of cosmological solutions can be addressed in massive gravity theories
with flat as well as with arbitrary reference metrics. I will first
review the exact isotropic solutions of the non-linear massive gravity
with flat reference metric. In this theory the effective
energy-momentum tensor arising from the mass term gives a cosmological
constant like contribution for any isotropic matter distribution.
However, metric perturbations around this solution do not have a mass
term of the Fierz-Pauli form. I will then discuss massive gravity with
arbitrary reference metric. We show that restoring the diffeomorphism
invariance in this theory by introducing the four Stueckelberg scalars
is equivalent to introducing an additional symmetry in the internal
space of the scalar fields. Thus for each particular choice of the
reference metric this gives a different generally covariant massive
gravity theory with different symmetries.
