Bounds on neutrino mass in viscous cosmology

Effective field theoretic description of dark matter fluid on large scales predicts viscosity of the order 10^-6 H<inf>0</inf> M<inf>P</inf>². Recently, it has been shown that the same magnitude of viscosity can resolve the discordance between large scale structure observations and Planck CMB data in the σ<inf>8</inf>-Ω<inf>m</inf>⁰ and H<inf>0</inf>-Ω<inf>m</inf>⁰ parameters space. On the other hand, massive neutrinos suppresses the matter power spectrum on the small length scales similar to the viscosities. Therefore, it is expected that the viscous dark matter setup along with massive neutrinos can provide stringent constraint on neutrino mass. In this article, we show that the inclusion of effective viscosity, which arises from summing over non linear perturbations at small length scales, indeed severely constrains the cosmological bound on neutrino masses. Under a joint analysis of Planck CMB and different large scale observation data, we find that upper bound on the sum of the neutrino masses, at 2-σ level, decreases respectively from ∑ m<inf>ν</inf> ≤ 0.396 eV (for normal hierarchy) and ∑ m<inf>ν</inf> ≤ 0.378 eV (for inverted hierarchy) to ∑ m<inf>ν</inf> ≤ 0.267 eV (for normal hierarchy) and ∑ m<inf>ν</inf> ≤ 0.146 eV (for inverted hierarchy).