Cosmological perturbations for two cold fluids in ΛcDM

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 ΛCDM Universe with cosmological constant Λ. 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 semiclassical approach to cosmic large-scale structure. In our companion paper, we apply these new theoretical results to generate novel higher order initial conditions for cosmological hydrodynamical simulations.