We study the spherical collapse model in dark energy cosmologies, in which dark energy is modelled as a minimally coupled scalar field. We first follow the standard assumption that dark energy does not cluster on the scales of interest. Investigating four different popular potentials in detail, we show that the predictions of the spherical collapse model depend on the potential used. We also in...

We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model is designed so that it predicts a relation between the peculiar velocity and density contrast that agrees with the results of N-body simulations in the regio...

A model is proposed of a collapsing quasi-spherical radiating star with matter content as shearfree isotropic fluid undergoing radial heat-flow with outgoing radiation. To describe the radiation of the system, we have considered both plane symmetric and spherical Vaidya solutions. Physical conditions and thermodynamical relations are studied using local conservation of momentum and surface red-...

We investigate a spherical overdensity model for the non-clustering dark energy (DE) with the constant equation of state, ωde in a flat universe. In this case, the exact solution for the evolution of the scale factor is obtained for general ωde. We also obtain the exact (when ωde = −13) and the approximate (when ωde 6= −13) solutions for the ratio of the overdensity radius to its value at the t...

We derive the asymptotic mass profile near the collapse center of an initial spherical density perturbation, δ ∝ M, of collision-less particles with non-radial motions. We show that angular momenta introduced at the initial time do not affect the mass profile. Alternatively, we consider a scheme in which a particle moves on a radial orbit until it reaches its turnaround radius, r∗. At turnaroun...

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-self-similar Tolman-Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular coordinates in the corresponding four dimensional spherical model.