Bianchi IX gravitational collapse of matter inhomogeneities

TL;DR

This paper models gravitational collapse of matter inhomogeneities using Bianchi IX spacetimes, exploring effects of anisotropies on collapse dynamics, curvature, and structure formation, with implications for halo density and pancake oscillations.

Contribution

It introduces a Bianchi IX-based model for gravitational collapse, linking anisotropic perturbations to standard collapse models and halo formation, and analyzes their impact on structure evolution.

Findings

Anisotropies shift the FLRW spatial curvature during collapse.

Effective EoS parameters for anisotropies are approximately -1/3 pre-virialization and 1/3 post-virialization.

Pancake structures exhibit oscillatory behavior in Bianchi IX spacetime.

Abstract

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution for a 1-dimensional perturbation. We study how these models are affected by small anisotropic perturbations within the BIX potential. For the spherical collapse case, we found that the model is equivalent to a closed FLRW Universe filled with matter and two perfect fluids representing the anisotropic contributions. From the linear evolution up to the turnaround, the anisotropies effectively shift the value of the FLRW spatial curvature, because the fluids have effective Equation of State (EoS) parameters $w \approx -1/3$. Then we estimate the impact of such anisotropies on the number density of haloes using the Press-Schechter formalism. If a fluid description of the anisotropies is still valid after virialization, the averaged over time EoS parameters are $w\approx 1/3$. Using this and demanding hydrostatic equilibrium, we find a relation between the mass $M$, the average radius $R$ and the pressure $p$ of the virialized final structure. When we consider perturbations of the Zeldovich solution, our qualitative analysis suggests that the so called \textit{pancakes} exhibit oscillatory behavior, as would be expected in the case of a vacuum BIX spacetime.