Exploring the self interacting dark matter properties from low redshift observations

We calculate the shear (eta) and bulk viscosity (zeta) of Self Interacting Dark Matter (SIDM) fluid using the kinetic theory formalism. Using the astrophysical constraints on dark matter self-interaction cross section over mass sigma/m, we demonstrate that viscous SIDM fluid violates the lower bound on the ratio of shear viscosity to its entropy density, eta/s = 1/4 pi. Then, considering the eta/s bound as universal, we derive a theoretical upper limit on the ratio of velocity average dark matter self interaction cross-section to its mass and also estimate an upper limit on SIDM mass. We report that mass of the SIDM particle should be sub-GeV scale. Furthermore, with the assumption of a power-law form of eta and zeta, we study its evolution in the light of low redshift observations. We show that at the large redshift, the SIDM viscosity is small, but at the small redshift, it becomes sufficiently large and contributes significantly to cosmic dissipation. As a consequence, viscous SIDM can explain the low redshift observations and also consistent with the standard cosmological prediction.