Dark Matter Cosmology with Varying Viscosity: A Possible Resolution to the S8 Tension

We study varying forms of viscous dark matter (DM) and try to address the intriguing tensions of the standard model of cosmology with recent cosmological data, including the Hubble and S-8 tensions. We note that by assuming the DM viscosity depends on the Hubble parameter, DM density, or both, one can improve the statistics. Although the models tend to aggravate the Hubble tension a bit, they tend to reduce the S-8 tension, even in comparison with the constant viscosity case. Since similar-to-viscosity massive neutrinos suppress the power spectrum of matter on small length scales, considering them along with the viscous DM, we find that the neutrino mass range is tightened.