Cosmological perturbations for two cold fluids in $\Lambda$CDM

TL;DR

This paper develops a detailed perturbation theory for two coupled cold fluids, baryons and dark matter, in the $mbda$CDM model, going beyond the single-fluid approximation to improve cosmological structure formation models.

Contribution

It introduces explicit recursion relations and all-order results for two-fluid perturbations, enhancing the theoretical framework for cosmic large-scale structure analysis.

Findings

Derived explicit recursion relations for two-fluid densities.

Provided all-order solutions in Lagrangian coordinates.

Connected theoretical results to initial conditions for simulations.

Abstract

The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing pressure, which is justified only for sufficiently large scales and late times. Here we go beyond the single-fluid approximation and develop the perturbation theory for two gravitationally coupled fluids while still assuming vanishing pressure. We mostly focus on perturbative expansions in powers of $D$ (or $D_+$), the linear structure growth of matter in a $\Lambda$CDM Universe with cosmological constant $\Lambda$. We derive in particular (1) explicit recursion relations for the two fluid densities, (2) complementary all-order results in the Lagrangian-coordinates approach, as well as (3) the associated component wavefunctions in a semi-classical approach to cosmic large-scale structure. In our companion paper (Hahn et al. 2020) we apply these new theoretical results to generate novel higher-order initial conditions for cosmological hydrodynamical simulations.