Minimal theory of massive gravity and constraints on the graviton mass

TL;DR

This paper investigates the minimal theory of massive gravity, focusing on the normal branch, and derives the strongest observational constraints on the graviton mass using cosmological data.

Contribution

It provides the first comprehensive constraint on the graviton mass within the normal branch of MTMG using multiple cosmological data sets.

Findings

The graviton mass is constrained to be less than 8.4×10⁻³⁴ eV at 95% CL.

The normal branch of MTMG shows deviations from General Relativity in background and perturbation dynamics.

The study offers the strongest bounds on graviton mass for this theory to date.

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.