2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/8792We studied the spherical collapse model in the flat $Λ$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.part of the numerical results changed, two typoes correctedAstrophysicstext