TY - JOUR

T1 - Splitting the spacetime

T2 - a systematic analysis of foliation dependence in cosmic averaging

AU - Mourier, Pierre

AU - Heinesen, Asta

N1 - Funding Information: This work is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement ERC advanced grant 740021-ARTHUS, PI: Thomas Buchert) in its earlier stages. It was also supported in early stages by Catalyst grant CSG-UOC1603 administered by the Royal Society of New Zealand. AH is funded by the Carlsberg foundation. PM acknowledges support and hospitality for a visit to the University of Canterbury within the context of the above Catalyst grant. In the later stages of this work, PM has been supported by the Universitat de les Illes Balears (UIB), Spain; the Spanish Agencia Estatal de Investigación grants PID2022-138626NB-I00, RED2022- 134204-E, and RED2022-134411-T, funded by MCIN/AEI/10.13039/501100011033/FEDER, UE; the MCIN with funding from the European Union NextGenerationEU/PRTR (PRTRC17.I1); the Comunitat Autonòma de les Illes Balears through the Direcció General de Recerca, Innovació I Transformació Digital with funds from the Tourist Stay Tax Law (PDR2020/11 — ITS2017-006), and the Conselleria d’Economia, Hisenda i Innovació grant number SINCO2022/6719.

PY - 2024/4/23

Y1 - 2024/4/23

N2 - It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries. In a cosmological context this is sometimes referred to as the averaging problem. At the heart of this problem in relativity is the non-uniqueness of the choice of foliation within which the statistical properties of the local spacetime are quantified, which can lead to ambiguity in the formulated average theory. This has led to debate in the literature on how to best construct and view such a coarse-grained hydrodynamic theory. Here, we address this ambiguity by performing the first quantitative investigation of foliation dependence in cosmological spatial averaging. Starting from the aim of constructing slicing-independent integral functionals (volume, mass, entropy, etc.) as well as average functionals (mean density, average curvature, etc.) defined on spatial volume sections, we investigate infinitesimal foliation variations and derive results on the foliation dependence of functionals and on extremal leaves. Our results show that one may only identify fully foliation-independent integral functionals in special scenarios, requiring the existence of associated conserved currents. We then derive bounds on the foliation dependence of integral functionals for general scalar quantities under finite variations within physically motivated classes of foliations. Our findings provide tools that are useful for quantifying, eliminating or constraining the foliation dependence in cosmological averaging.

AB - It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries. In a cosmological context this is sometimes referred to as the averaging problem. At the heart of this problem in relativity is the non-uniqueness of the choice of foliation within which the statistical properties of the local spacetime are quantified, which can lead to ambiguity in the formulated average theory. This has led to debate in the literature on how to best construct and view such a coarse-grained hydrodynamic theory. Here, we address this ambiguity by performing the first quantitative investigation of foliation dependence in cosmological spatial averaging. Starting from the aim of constructing slicing-independent integral functionals (volume, mass, entropy, etc.) as well as average functionals (mean density, average curvature, etc.) defined on spatial volume sections, we investigate infinitesimal foliation variations and derive results on the foliation dependence of functionals and on extremal leaves. Our results show that one may only identify fully foliation-independent integral functionals in special scenarios, requiring the existence of associated conserved currents. We then derive bounds on the foliation dependence of integral functionals for general scalar quantities under finite variations within physically motivated classes of foliations. Our findings provide tools that are useful for quantifying, eliminating or constraining the foliation dependence in cosmological averaging.

KW - cosmological parameters from LSS

KW - Cosmological perturbation theory in GR and beyond

KW - dark energy theory

UR - http://www.scopus.com/inward/record.url?scp=85191308946&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2401.09170

DO - 10.48550/arXiv.2401.09170

M3 - Article

AN - SCOPUS:85191308946

VL - 2024

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 4

M1 - 067

ER -