Coarse-Grained Cosmological Perturbation Theory
  Semi-analytical methods, based on Eulerian perturbation theory, are a
promising tool to follow the time evolution of cosmological perturbations at
small redshifts and at mildly nonlinear scales. All these schemes are based on
two approximations: the existence of a smoothing scale and the single-stream
approximation, where velocity dispersion of the dark matter fluid, as well as
higher moments of the particle distributions, are neglected. Despite being
widely recognized, these two assumptions are, in principle, incompatible, since
any finite smoothing scale gives rise to velocity dispersion and higher moments
at larger scales. We describe a new approach to perturbation theory, where the
Vlasov and fluid equations are derived in presence of a finite coarse-graining
scale: this allows a clear separation between long and short distance modes and
leads to a hybrid approach where the former are treated perturbatively and the
effect of the latter is encoded in external source terms for velocity, velocity
dispersion, and all the higher order moments, which can be computed from N-body
simulations. We apply the coarse-grained perturbation theory to the computation
of the power spectrum and the cross-spectrum between density and velocity
dispersion, and compare the results with N-body simulations, finding good
agreement.
