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Cosmology and Nongalactic Astrophysics · arXiv:2409.00024 v1 · submitted 16 Aug 2024

Cosmic averaging over multiscaled structure: on foliations, gauges and backreaction

Dave B. H. Verweg, Bernard J. T. Jones, Rien van de Weygaert

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“In this paper we demonstrate that the implied backreaction terms are artificial, that is gauge dependent, which may easily cause ambiguous estimates of its significance.”

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The paper

Abstract

The observation that accelerated cosmic expansion is dominant since the Mega-parsec cosmic structure became nonlinear seems like an extraordinary coincidence, unless the acceleration is somehow driven by the emergence of the structure. That has given rise to the controversial concept of a gravitational backreaction through which inhomogeneity becomes a driver of accelerated expansion. The standard route when studying strongly inhomogeneous cosmological models is to take either a perturbative approach or a spatial averaging approach. Here we argue that because backreaction is in fact a nonlinear multiscale phenomenon, perturbative approaches may have a limited validity. The alternative is the proposed averaging approach. In this paper we demonstrate that the implied backreaction terms are artificial, that is gauge dependent, which may easily cause ambiguous estimates of its significance. In the current study, we forward a formal fully geometric framework of cosmic foliations in the context of relativistic cosmology. Here we show that fixing a foliation of spacetime determines a choice of gauge. Addressing the correspondence between the metric tensor and the foliation allows us to clarify the theoretical implications of choosing a foliation. Within the context of backreaction, this formalism allows us to discuss the complications of averaging. It reveals that spatial averaging can induce artificial backreaction terms that arise from any specific choice of gauge. Averaging methods presented so far all encounter this problem. Within our foliation framework, we can produce a gauge invariant method of averaging by considering a group of proper time foliations which any cosmic observe can agree upon. We demonstrate that this implies the gauge invariance of the averaging procedure. This makes it applicable to standard cosmological simulations.

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abstract compiled · 2026-09-23 · no language-model review

How the main claim is stated: asserted 0.89

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.84 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
The observation that accelerated cosmic expansion is dominant since the Mega-parsec cosmic structure became nonlinear seems like an extraordinary coincidence, unless the acceleration is somehow driven by the emergence of the structure. background 1.00 0.06 0.04 hedged possibility 0.60
That has given rise to the controversial concept of a gravitational backreaction through which inhomogeneity becomes a driver of accelerated expansion. background 1.00 0.03 0.03 asserted 0.90
The standard route when studying strongly inhomogeneous cosmological models is to take either a perturbative approach or a spatial averaging approach. background 1.00 0.04 0.02 asserted 0.99
Here we argue that because backreaction is in fact a nonlinear multiscale phenomenon, perturbative approaches may have a limited validity. background 0.58 0.20 0.06 hedged possibility 0.98
The alternative is the proposed averaging approach. background 0.68 0.07 0.04 asserted 0.82
In this paper we demonstrate that the implied backreaction terms are artificial, that is gauge dependent, which may easily cause ambiguous estimates of its significance. result 0.95 0.61 0.51 asserted 0.89
In the current study, we forward a formal fully geometric framework of cosmic foliations in the context of relativistic cosmology. contribution 0.93 0.84 0.05 asserted 0.99
Here we show that fixing a foliation of spacetime determines a choice of gauge. result 0.70 0.79 0.09 asserted 1.00
Addressing the correspondence between the metric tensor and the foliation allows us to clarify the theoretical implications of choosing a foliation. contribution 0.48 0.77 0.06 asserted 0.71
Within the context of backreaction, this formalism allows us to discuss the complications of averaging. contribution 0.61 0.55 0.05 asserted 0.77
It reveals that spatial averaging can induce artificial backreaction terms that arise from any specific choice of gauge. result 0.82 0.72 0.34 asserted 0.99
Averaging methods presented so far all encounter this problem. background 0.45 0.10 0.07 asserted 1.00
Within our foliation framework, we can produce a gauge invariant method of averaging by considering a group of proper time foliations which any cosmic observe can agree upon. method 0.53 0.90 0.28 asserted 0.71
We demonstrate that this implies the gauge invariance of the averaging procedure. result 0.63 0.92 0.24 asserted 1.00
This makes it applicable to standard cosmological simulations. interpretation 0.93 0.60 0.09 asserted 0.87

What kind of paper the classifier reports this is: method or tool 0.54 · evidence from proof or derivation 0.88

What was examined, and what was not

Sources read

  • arXiv listing abstract v1

Not examined

  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers

Levels run

  • P abstract

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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 10,614 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

What it cites · 101 sentences without a confident label

Contests 1 paper
Uses the method or tool of 3 papers
  • To overcome this problem, Gasperini et al. [ref] construct and utilize an averaging procedure, [equation] where $S = S ∘ϕ^-1$ and $h = h ∘ϕ^-1$ with $ϕ$ being the map $ϕ(t, x) = (ϕ^1(t,x), x ) = (τ, x)$ such that the foliation are now slices over $ϕ(t, x) =const$.

    Gauge invariant averages for the cosmological backreaction · Gauge-invariant averaging: the Gasperini suggestion · 0.88

  • To overcome this problem, Gasperini et al. [ref] construct and utilize an averaging procedure, [equation] where $S = S ∘ϕ^-1$ and $h = h ∘ϕ^-1$ with $ϕ$ being the map $ϕ(t, x) = (ϕ^1(t,x), x ) = (τ, x)$ such that the foliation are now slices over $ϕ(t, x) =const$.

    A covariant and gauge invariant formulation of the cosmological "backreaction" · Gauge-invariant averaging: the Gasperini suggestion · 0.88

  • To overcome this problem, Gasperini et al. [ref] construct and utilize an averaging procedure, [equation] where $S = S ∘ϕ^-1$ and $h = h ∘ϕ^-1$ with $ϕ$ being the map $ϕ(t, x) = (ϕ^1(t,x), x ) = (τ, x)$ such that the foliation are now slices over $ϕ(t, x) =const$.

    Light-cone averaging in cosmology: formalism and applications · Gauge-invariant averaging: the Gasperini suggestion · 0.88

Compares with 1 paper
  • Relating to literature on the backreaction, we contrast this to the discussion in e.g. Buchert & Räsänen [ref] , where perturbation-gauge transformations $δT ↦δT$, coordinate transformations $x^μ↦x^μ$ and foliation transformation $F ↦F$ (discussed below) are seen as independent constructions.

    Backreaction in late-time cosmology · Relativistic cosmology as gauge theory · 0.82

Cites as support 8 papers
Cites as background 39 papers

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