A few numbers from the turnaround epoch of collapse

TL;DR

This paper investigates the turnaround phase of gravitational collapse using relativistic Lagrangian perturbation theory, revealing universal parameters and differences from traditional models.

Contribution

It introduces a relativistic Lagrangian approach to analyze the turnaround epoch, highlighting scale-independent parameters and discrepancies with Eulerian perturbation models.

Findings

The density contrast at turnaround is smaller than in spherical models.

Backreaction effects are comparable to energy density.

Universal parameters are identified across various initial conditions.

Abstract

The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a wide variety of initial conditions. In particular, the density contrast of the collapsing domain at the turnaround is shown to be significantly smaller than the value provided by Eulerian perturbative (homogeneous and spherical) model. Combined curvature and kinematical backreaction are shown to be of the order of the energy density. Possible improvements of our treatment are put into perspective.