Beyond Spherical Top Hat Collapse

TL;DR

This paper generalizes the spherical top hat collapse model by deriving a dynamical equation for inhomogeneous spherical perturbations within the Lemaitre-Tolman-Bondi framework, including solutions with a cosmological constant.

Contribution

It introduces a generalized approach to model inhomogeneous spherical perturbations, extending the classical top hat collapse to more complex initial profiles and cosmological settings.

Findings

Derived a dynamical equation for density contrast evolution.

Constructed solutions with and without a cosmological constant.

Enhanced understanding of inhomogeneous spherical collapse dynamics.

Abstract

We study the evolution of inhomogeneous spherical perturbations in the universe in a way that generalizes the spherical top hat collapse in a straightforward manner. For that purpose we derive a dynamical equation for the evolution of the density contrast in the context of a Lemaitre-Tolman-Bondi metric and construct solutions with and without a cosmological constant for the evolution of a spherical perturbation with a given initial radial profile.