Spherical collapse of non-top-hat profiles in the presence of dark energy with arbitrary sound speed

TL;DR

This paper investigates the nonlinear spherical collapse of matter in the presence of dark energy with arbitrary sound speed, revealing effects on matter profiles, velocities, and potential, and identifying pathological behaviors in certain dark energy models.

Contribution

It introduces a pseudo-spectral numerical method to accurately solve nonlinear collapse equations with arbitrary dark energy sound speeds, extending previous analytical and numerical results.

Findings

Dark energy fluctuations significantly affect matter profiles and velocities.

Low sound speed phantom dark energy can cause negative energy densities around halos.

The virialization threshold depends on dark energy sound speed, confirming and extending prior results.

Abstract

We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. The model is described by a system of partial differential equations solved using a pseudo-spectral method with collocation points. This method can reproduce the known analytical solutions in the linear regime with an accuracy better than $10^{-6}\%$ and better than $10^{-2}\%$ for the virialization threshold given by the usual spherical collapse model. We show the impact of nonlinear dark energy fluctuations on matter profiles, matter peculiar velocity and gravitational potential. We also show that phantom dark energy models with low sound speed can develop a pathological behaviour around matter halos, namely negative energy density. The dependence of the virialization threshold density for collapse on the dark energy sound speed is also computed, confirming and extending previous results in the limit for homogeneous and clustering dark energy.