GRG Editor's Choice: On average properties of inhomogeneous fluids in general relativity III. General fluid cosmologies

© SpringerBuchert, T., Mourier, P. & Roy, X. On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies. Gen Relativ Gravit 52, 27 (2020).

Editor's Choice (Research Article)

Published: 12 March 2020

"I can recommend this paper for Editor's Choice. I think that it is a `tour-de-force' and that it gives what is probably the `final' presentation of frame-dependence in scalar averaging in GR, an issue whose lack of clarity has plagued the topic for years." (Handling Editor)


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.

The authors: 

The authors have been collaborating on research in cosmology at the Centre de Recherche Astrophysique de Lyon, France. Thomas Buchert supervised the PhD projects of Pierre Mourier (2019) and Xavier Roy (2011). 

Thomas Buchert's previous articles on "Dust Cosmologies" (Paper I, 2000) and "Perfect Fluid Cosmologies" (Paper II, 2001) are two of the most cited works in the journal General Relativity and Gravitation

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.