Bounds on Neutrino Mass in Viscous Cosmology

Effective field theory of dark matter fluid on large scales predicts the presence of viscosity of the order of $10^{-6} H_0 M_P^2$. It has been shown that this magnitude of viscosities can resolve the discordance between large scale structure observations and Planck CMB data in the $\sigma_8$-$\Omega_m^0$ and $H_0$-$\Omega_m^0$ parameters space. Massive neutrinos suppresses the matter power spectrum on the small length scales similar to the viscosities. We show that by including the effective viscosity, which arises from summing over non linear perturbations at small length scales, 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-$\sigma$ level, decreases from $\sum m_\nu \le 0.396\,$eV (normal hierarchy) and $\sum m_\nu \le 0.378 \,$eV (inverted hierarchy) to $\sum m_\nu \le 0.267\,$eV (normal hierarchy) and $\sum m_\nu \le 0.146\,$eV (inverted hierarchy) when the effective viscosities are included.