Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the maximum volume of collapsing structures   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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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas