Physical approximations for the nonlinear evolution of perturbations in dark energy scenarios

TL;DR

This paper compares two approximate methods for modeling the nonlinear evolution of dark energy perturbations, highlighting their equivalence and consistency with general relativity in the linear regime.

Contribution

It demonstrates that the spherical collapse and pseudo-Newtonian schemes produce identical equations for density contrast when using an effective sound speed.

Findings

Both schemes yield identical equations for density contrast.

The approximations are consistent with linearized general relativity.

The comparison supports the validity of these approximate approaches.

Abstract

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy as well, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model, and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.