Coarse-grained cosmological perturbation theory: stirring up the dust model

TL;DR

This paper develops a coarse-grained cosmological perturbation theory for pressureless fluids, deriving new recursion relations and analyzing the impact on power spectra, including vorticity, with results aligning well with simulations.

Contribution

It introduces a novel coarse-grained dust model with recursion relations for perturbation kernels, bridging Eulerian and Lagrangian frameworks in cosmological perturbation theory.

Findings

Derived vorticity power spectrum from first principles.

Achieved good agreement with N-body simulation measurements.

Provided a method to map Eulerian kernels to Lagrangian space.

Abstract

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.