The spherical collapse model and cluster formation beyond the $\Lambda$ cosmology: Indications for a clustered dark energy?

TL;DR

This paper extends the spherical collapse model to include evolving dark energy, examining how clustered versus homogeneous dark energy affects galaxy cluster formation, concentration, and consistency with observations.

Contribution

It provides a comprehensive formulation of nonlinear structure formation with evolving dark energy, highlighting the impact of dark energy clustering on cluster properties.

Findings

Cluster formation occurs at redshift z~1-2.

Clustered dark energy leads to more concentrated structures.

Homogeneous dark energy models do not match observed cluster concentrations.

Abstract

We generalize the small scale dynamics of the universe by taking into account models with an equation of state which evolves with time, and provide a complete formulation of the cluster virialization attempting to address the nonlinear regime of structure formation. In the context of the current dark energy models, we find that galaxy clusters appear to form at z\sim 1-2, in agreement with previous studies. Also, we investigate thoroughly the evolution of spherical matter perturbations, as the latter decouple from the background expansion and start to ``turn around'' and finally collapse. Within this framework, we find that the concentration parameter depends on the choice of the considered dark energy (homogeneous or clustered). In particular, if the distribution of the dark energy is clustered then we produce more concentrated structures with respect to the homogeneous dark energy. Finally, comparing the predicted concentration parameter with the observed concentration parameter, measured for four massive galaxy clusters, we find that the scenario which contains a pure homogeneous dark energy is unable to reproduce the data. The situation becomes somewhat better in the case of an inhomogeneous (clustered) dark energy.