Spherical collapse in the extended quintessence cosmological models

TL;DR

This study examines the non-linear evolution of matter density perturbations in extended quintessence dark energy models using spherical collapse, finding minimal differences from the standard $\\Lambda$CDM model and between the metric and Palatini formalisms.

Contribution

It provides a detailed analysis of spherical collapse in extended quintessence models, showing negligible differences from $\\Lambda$CDM and between formalisms, aiding understanding of structure formation.

Findings

Deviations from $\\Lambda$CDM are less than 1% for negative coupling constants.

Differences between metric and Palatini formalisms are very small.

Quantities like $\\delta_c$ and $\\Delta_v$ are unaffected by formalism choice.

Abstract

We use the spherical collapse method to investigate the non-linear density perturbations of pressureless matter in the cosmological models with the extended quintessence as dark energy in the metric and Palatini formalisms. We find that for both formalisms, when the coupling constant is negative, the deviation from the $\Lambda$CDM model is the least according to the evolutionary curves of the linear density contrast $\delta_{c}$ and virial overdensity $\Delta_{v}$, and it is less than one percent. And this indicates that, in the extended quintessence cosmological models in which the coupling constant is negative, all quantities dependent on $\delta_{c}$ or $\Delta_{v}$ are essentially unaffected if the linear density contrast or the virial overdensity of the $\Lambda$CDM model is used as an approximation. Moreover, we find that the differences between different formalisms are very small in terms of structure formation, and thus can not be used to distinguish the metric and Palatini formalisms.