  Following an approach of Matarrese and Pietroni, we derive the functional
renormalization group (RG) flow of the effective action of cosmological
large-scale structures. Perturbative solutions of this RG flow equation are
shown to be consistent with standard cosmological perturbation theory.
Non-perturbative approximate solutions can be obtained by truncating the a
priori infinite set of possible effective actions to a finite subspace. Using
for the truncated effective action a form dictated by dissipative fluid
dynamics, we derive RG flow equations for the scale dependence of the effective
viscosity and sound velocity of non-interacting dark matter, and we solve them
numerically. Physically, the effective viscosity and sound velocity account for
the interactions of long-wavelength fluctuations with the spectrum of
smaller-scale perturbations. We find that the RG flow exhibits an attractor
behaviour in the IR that significantly reduces the dependence of the effective
viscosity and sound velocity on the input values at the UV scale. This allows
for a self-contained computation of matter and velocity power spectra for which
the sensitivity to UV modes is under control.
