Viscous Self Interacting Dark Matter and Cosmic Acceleration

Abstract: Self interacting dark matter (SIDM) provides us with a consistent solution to certain astrophysical observations in conflict with collision-less cold DM paradigm. In this work we estimate the shear viscosity $(\eta)$ and bulk viscosity $(\zeta)$ of SIDM, within kinetic theory formalism, for galactic and cluster size SIDM halos. To that extent we make use of the recent constraints on SIDM crossections for the dwarf galaxies, LSB galaxies and clusters. We also estimate the change in solution of Einstein's equation due to these viscous effects and find that $\sigma/m$ constraints on SIDM from astrophysical data provide us with sufficient viscosity to account for the observed cosmic acceleration at present epoch, without the need of any additional dark energy component. Using the estimates of dark matter density for galactic and cluster size halo we find that the mean free path of dark matter $\sim$ few Mpc. Thus the smallest scale at which the viscous effect start playing the role is cluster scale. Astrophysical data for dwarf, LSB galaxies and clusters also seems to suggest the same. The entire analysis is independent of any specific particle physics motivated model for SIDM.