Minimal theory of massive gravity and constraints on the graviton mass

Abstract: 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 $\Lambda$CDM; 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 $\mu_{0}$, finding that $(\mu_{0}/H_{0})^{2}=0.119_{-0.098}^{+0.12}$ at $68\%$ CL, which in turn gives an upper bound at $95\%$ CL as $\mu_{0}<8.4\times10^{-34}$ eV. This corresponds to the strongest bound on the mass of the graviton for the normal branch of MTMG.