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arXiv · 2112.05245

On the maximum volume of collapsing structures

Jan J. Ostrowski·Ismael Delgado Gaspar
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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.

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Jan J. Ostrowski, Ismael Delgado Gaspar. 2021-12-09. On the maximum volume of collapsing structures. https://doi.org/10.1088/1475-7516%2F2022%2F04%2F059

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