Spherical Collapse Model
  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. 
Ding-fang Zeng and Yi-hong Gao