The spherical collapse model in time varying vacuum cosmologies

TL;DR

This paper extends the spherical collapse model to cosmologies with a time-varying vacuum energy, analyzing how different vacuum energy distributions affect structure formation and concentration.

Contribution

It generalizes the spherical collapse model for vacuum energy that varies with the Hubble rate, especially for quadratic models like the quantum field vacuum, and explores the impact of vacuum clustering.

Findings

Vacuum energy properties influence the virial density and collapse factor.

Clustered vacuum energy can lead to more concentrated cosmic structures.

The model's expansion history closely resembles standard $\\Lambda$CDM cosmology.

Abstract

We investigate the virialization of cosmic structures in the framework of flat FLRW cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around" and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, $\Lambda=\Lambda(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $\Lambda(H)$ is a quadratic function, $\Lambda(H)=n_0+n_2\,H^2$, with $n_0\neq 0$. This model was previously studied by our team using the latest high quality cosmological data to constrain its free parameters, as well as the predicted cluster formation rate. It turns out that the corresponding Hubble expansion history resembles that of the traditional $\Lambda$CDM cosmology. We use this $\Lambda(t)$CDM framework to illustrate the fact that the properties of the spherical collapse model (virial density, collapse factor, etc.) depend on the choice of the considered vacuum energy (homogeneous or clustered). In particular, if the distribution of the vacuum energy is clustered, then, under specific conditions, we can produce more concentrated structures with respect to the homogeneous vacuum energy case.