Graviton mass might reduce tension between early and late time cosmological data

The standard $\Lambda$-CDM predicts a growth of structures which tends to be higher than the values of redshift space distortion (RSD) measurements, if the cosmological parameters are fixed by the CMB data. In this paper we point out that this discrepancy can be resolved/understood if we assume that the graviton has a small but non-zero mass. In the context of the Minimal Theory of Massive Gravity (MTMG), due to infrared Lorentz violations measurable only at present cosmological scales, the graviton acquires a mass without being haunted by unwanted extra degrees of freedom. While the so-called self-accelerating branch of cosmological solutions in MTMG has the same phenomenology for the background as well as the scalar- and vector-type linear perturbations as the $\Lambda$-CDM in General Relativity (GR), it is possible to choose another branch so that the background is the same as that in GR but the evolution of matter perturbations gets modified by the graviton mass. On studying the fit of such modified dynamics to the above-mentioned RSD measurements, we find that the $\Lambda$-CDM model is less probable than MTMG by two orders of magnitude. With the help of the cross correlation between the integrated Sachs-Wolfe (ISW) effect and the large scale structure (LSS), the data also pin-down the graviton mass squared around $\mu^2\approx - (3\times 10^{-33} \rm{eV})^2$, which is consistent with the latest bound $|\mu^2|<(1.2\times 10^{-22} \rm{eV})^2$ set by the recent LIGO observation.