On the maximum volume of collapsing structures

TL;DR

This paper introduces a new method to determine the maximum volume of collapsing cosmological structures without assuming symmetry, using scalar averaging and Lagrangian perturbations, improving upon traditional spherical models.

Contribution

It presents a novel approach combining scalar averaging and Lagrangian perturbations to estimate maximum collapse volume without symmetry constraints.

Findings

Derived a maximum volume bound for collapse models.

Compared results with exact inhomogeneous solutions.

Discussed potential extensions of the method.

Abstract

In many cosmological models, including the $\Lambda$CDM concordance model, there exist a theoretical upper bounds on the size of collapsing structures. The most common formulations in the literature refer to a turnaround radius in spherical symmetry or a turnaround surface, defined as the zero-expansion boundary separating the outer Hubble flow from the inner flow of a collapsing fluid. In order to access a generic scenario, we propose an improvement of this cosmological test in terms of the maximum volume of the cosmological structures, which is equivalent to a zero-averaged expansion -- instead of the zero-local expansion. By combining the Lagrangian perturbations method and the scalar averaging of Einstein's equations, we obtain a maximum volume for a collapse model without any restricting symmetries. We compare this result with some exact, inhomogeneous solutions and discuss further potential developments.