Virialization in Dark Energy Cosmology

We discuss the issue of energy nonconservation in the virialzation process of spherical collapse model with homogeneous dark energy. We propose an approximation scheme to find the virialization radius as well as modify a scheme recently proposed by Maor and Lahav. By comparing various schemes and estimating the parameter q, we conclude that the problem of energy conservation may have sizable effect in fitting models to observations. Subject headings: cosmology:theory-galaxies:clusters:general-large-scale structure of universe-galaxies:formation Analyzing the effects of dark energy on the nonlinear structure formation process may provide us new ways of constraining the properties of dark energy. Especially, a lot of recent works focused on analyzing the effects of dark energy in the framework of the spherical collapse model (Lahav et al. 1991; Wang & Steinhardt 1998; Maor & Lahav 2005; Mota & de Bruck 2004; Horellou & Berge 2005; Battye & Weller 2003; Iliev & Shapiro 2001; Weinberg & Kamionkowski 2003; Nunes & Mota 2004). The spherical collapse model is a simple but powerful framework to understand the growth of bound systems in the universe (Gunn & Gott 1972). It is also incorporated in the famous Press-Schecter formalism (Press & Schechter 1974). In spherical collapse model, we consider a top-hat spherical overdensity with massM and radius R. At early times, it expands along with the Hubble flow and density perturbations grow proportionally to the scale factor. After the perturbation exceeds a critical value, the spherical overdensity region will decouple from the Hubble flow and go through three phases: (1) expansion to a maximum radius, Rta, after which the overdensity will turn-around to collapse; (2) collapse; (3) virialization at the virialization radius Rvir. This address will be valid after Sep. 21, 2005