Resummed propagators in multi-component cosmic fluids with the eikonal approximation

TL;DR

This paper develops an eikonal approximation method to analyze how large-scale motions influence small-scale evolution in multi-component cosmic fluids, extending previous single-fluid results and examining the effects of isodensity modes.

Contribution

The paper introduces an eikonal approximation for multi-component cosmic fluids, deriving resummed propagators and analyzing the impact of isodensity modes on small-scale dynamics.

Findings

Resummed propagators for single and multi-fluid cases are obtained.

Isodensity modes affect both phase and amplitude of small-scale modes.

Small corrections are found for CDM-baryon mixing due to isodensity modes.

Abstract

We introduce the eikonal approximation to study the effect of the large-scale motion of cosmic fluids on their small-scale evolution. This approach consists in collecting the impact of the long-wavelength displacement field into a single or finite number of random variables, whose statistical properties can be computed from the initial conditions. For a single dark matter fluid, we show that we can recover the nonlinear propagators of renormalized perturbation theory. These are obtained with no need to assume that the displacement field follows the linear theory. Then we extend the eikonal approximation to many fluids. In particular, we study the case of two non-relativistic components and we derive their resummed propagators in the presence of isodensity modes. Unlike the adiabatic case, where only the phase of small-scale modes is affected by the large-scale advection field, the isodensity modes change also the amplitude on small scales. We explicitly solve the case of cold dark matter-baryon mixing and find that the isodensity modes induce only very small corrections to the resummed propagators.