Spherical Collapse Model

TL;DR

This paper presents an analytical approach to the spherical collapse model within flat Lambda-CDM cosmology, providing exact formulas for key parameters used in structure formation theories.

Contribution

It introduces precise analytical formulas for the critical density contrast and density ratios at virialization, enhancing the accuracy of Press-Schechter theory applications.

Findings

Exact formulas for critical density contrast derived

Analytical expressions for density ratios at virialization obtained

Formulas can be solved precisely using numerical methods

Abstract

We studied the spherical collapse model in the flat $\Lambda$CDM cosmology and provided exact and analytical formulaes for the calculation of the two important parameters in the application of Press-Schechter theory, the critical density contrast and the ratio of cluster/background densities at the virialization point in terms of a media variable which can be solved precisely by numerical methods.