Coarse-grained cosmological perturbation theory: stirring up the dust
  model
  We study the effect of coarse-graining the dynamics of a pressureless
selfgravitating fluid (coarse-grained dust) in the context of cosmological
perturbation theory, both in the Eulerian und Lagrangian framework. We obtain
recursion relations for the Eulerian perturbation kernels of the coarse-grained
dust model by relating them to those of the standard pressureless fluid model.
The effect of the coarse-graining is illustrated by means of power and cross
spectra for density and velocity that are computed up to 1-loop order. In
particular, the large scale vorticity power spectrum that arises naturally from
a mass-weighted velocity is derived from first principles. We find
qualitatively good agreement of the magnitude, shape and spectral index of the
vorticity power spectrum with recent measurements from N-body simulations and
results from the effective field theory of large scale structure. To lay the
ground for applications in the context of Lagrangian perturbation theory we
finally describe how the kernels obtained in Eulerian space can be mapped to
Lagrangian ones.
