Formation of cosmological mass condensation within a FRW universe: exact general relativistic solutions

TL;DR

This paper presents exact general relativistic solutions for matching inhomogeneous overdense regions to a FRW universe, revealing the necessity of thin shells and intermediate underdense regions in the process.

Contribution

It provides a rigorous analysis of the matching conditions in spherical symmetric pressure-free models, highlighting the role of thin shells and underdense regions, which were previously overlooked.

Findings

Matching generally requires a thin shell.

An intermediate underdense region always appears in subhorizon cases.

Exact solutions clarify the structure of mass condensations in cosmology.

Abstract

Within the framework of an exact general relativistic formulation of gluing manifolds, we consider the problem of matching an inhomogeneous overdense region to a Friedmann-Robertson-Walker background universe in the general spherical symmetric case of pressure-free models. It is shown that, in general, the matching is only possible through a thin shell, a fact ignored in the literature. In addition to this, in subhorizon cases where the matching is possible, an intermediate underdense region will necessarily arise.