Large scale structure from viscous dark matter

Cosmological perturbations of sufficiently long wavelength admit a fluid dynamic description. We consider modes with wavevectors below a scale k_m for which the dynamics is only mildly non-linear. The leading effect of modes above that scale can be accounted for by effective non-equilibrium viscosity and pressure terms. For mildly non-linear scales, these mainly arise from momentum transport within the ideal and cold but inhomogeneous fluid, while momentum transport due to more microscopic degrees of freedom is suppressed. As a consequence, concrete expressions with no free parameters, except the matching scale k_m, can be derived from matching evolution equations to standard cosmological perturbation theory. Two-loop calculations of the matter power spectrum in the viscous theory lead to excellent agreement with N-body simulations up to scales k=0.2 h/Mpc. The convergence properties in the ultraviolet are better than for standard perturbation theory and the results are robust with respect to variations of the matching scale