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  On Average Properties of Inhomogeneous Fluids in General Relativity III: General Fluid Cosmologies

Buchert, T., Mourier, P., & Roy, X. (2020). On Average Properties of Inhomogeneous Fluids in General Relativity III: General Fluid Cosmologies. General Relativity and Gravitation, 52(3): 27. doi:10.1007/s10714-020-02670-6.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-9184-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-F391-4
Genre: Journal Article

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 Creators:
Buchert , Thomas, Author
Mourier, Pierre1, Author              
Roy , Xavier, Author
Affiliations:
1Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24011              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO
 Abstract: We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper~I) and irrotational perfect fluids (Paper~II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers~I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers~I and II and focuses on the fluid flow and the associated $1+3$ threading congruence, used jointly with the $3+1$ foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.

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 Dates: 2019-12-092020
 Publication Status: Published in print
 Pages: 67 pages, 4 figures, 1 table
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 Rev. Method: -
 Identifiers: arXiv: 1912.04213
URI: http://arxiv.org/abs/1912.04213
DOI: 10.1007/s10714-020-02670-6
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Title: General Relativity and Gravitation
Source Genre: Journal
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Pages: - Volume / Issue: 52 (3) Sequence Number: 27 Start / End Page: - Identifier: -