# Top-Hat Spherical Collapse with Clustering Dark Energy. I. Radius Evolution and Critical Contrast Density

## TL;DR

This paper investigates how clustering dark energy affects the evolution of spherical collapse in cosmology, focusing on the critical density and radius changes with respect to the clustering parameter.

## Contribution

It introduces a generalized Top-Hat Spherical Collapse model incorporating dark energy clustering via a free parameter, accounting for energy conservation issues.

## Key findings

- Critical contrast density depends on dark energy clustering.
- Radius evolution is significantly influenced by the clustering parameter.
- Model provides new insights into structure formation with clustered dark energy.

## Abstract

Understanding the influence of dark energy on the formation of structures is currently a major challenge in Cosmology, since it can distinguish otherwise degenerated viable models. In this work we consider the Top-Hat Spherical-Collapse (SC) model with dark energy, which can partially (or totally) cluster, according to a free parameter $\gamma$. The {\it lack of} energy conservation has to be taken into account accordingly, as we will show. We determine characteristic quantities for the SC model, such as the critical contrast density and radius evolution, with particular emphasis on their dependence on the clustering parameter $\gamma$.