Minimal theory of massive gravity in the light of CMB data and the S8 tension

Abstract

We investigate the minimal theory of massive gravity (MTMG) in the light of different observational datasets that are in tension within the $\mathrm{\ensuremath{\Lambda}}$ cold dark matter cosmology. In particular, we analyze the MTMG model, for the first time, with the Planck--cosmic microwave background (CMB) data, and how these precise measurements affect the free parameters of the theory. The MTMG model can affect the CMB power spectrum at large angular scales and cause a suppression on the amplitude of the matter power spectrum. We find that on adding Planck-CMB data, the graviton has a small, positive, but nonzero mass at 68% confidence level, and from this perspective, we show that the tension between redshift space distortions measurements and Planck-CMB data in the parametric space ${S}_{8}\ensuremath{-}{\mathrm{\ensuremath{\Omega}}}_{m}$ can be resolved within the MTMG scenario. Through a robust and accurate analysis, we find that the ${H}_{0}$ tension between the CMB and the local distance ladder measurements still remains but can be reduced to $\ensuremath{\sim}3.5\ensuremath{\sigma}$ within the MTMG theory. The MTMG is very well consistent with the CMB observations, and undoubtedly, it can serve as a viable candidate among other modified gravity theories.