We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.
Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution with a special singular reference metric. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear perturbations. We find that the graviton ray can be null in massive gravity by considering full back reaction of the massive gravitational waves to the metric. We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton.
The Minimal theory of Massive Gravity (MTMG) is endowed non-linearly
with only two tensor modes in the gravity sector which acquire a non-zero
mass. On a homogeneous and isotropic background the theory is known
to possess two branches: the self-accelerating branch with a phenomenology
in cosmology which, except for the mass of the tensor modes, exactly
matches the one of ΛCDM; and the normal branch which instead
shows deviation from General Relativity in terms of both background
and linear perturbations dynamics. For the latter branch we study
using several early and late times data sets the constraints on today's
value of the graviton mass μ0, finding that (μ0/H
0)2 = 0.119-0.098
at 68% CL, which in turn gives an upper bound at 95% CL as μ0 < 8.4 × 10-34 eV. This corresponds to the strongest bound on the mass of the graviton
for the normal branch of MTMG.