An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution

TL;DR

This paper introduces an enhanced semi-analytical spherical collapse model that accounts for non-spherical effects and shell crossing, aligning well with N-body simulations and including dark energy influences.

Contribution

It presents a novel extension of the spherical collapse model that incorporates deviations from sphericity, shell crossing, and dark energy effects, improving accuracy in non-linear structure formation.

Findings

Model predictions match N-body simulation results.

Pre-turnaround predictions nearly identical to standard model.

Includes effects of dark energy on collapse dynamics.

Abstract

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 region where such a comparison can sensibly be made. Prior to turnaround, when the unmodified spherical collapse model is expect to be a good approximation, the predictions of the two models coincide almost exactly. The effects of a late time dominating dark energy component are also taken into account. The improved spherical collapse model is a useful tool when one requires a good approximation not just to the evolution of the density contrast but also its trajectory. Moreover, the analytical fitting formulae presented is simple enough to be used anywhere where the standard spherical collapse might be used but with the advantage that it includes a realistic model of the effects of virialisation.