Applicability of the linearly perturbed FRW metric and Newtonian cosmology

Syksy Rasanen

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Applicability of the linearly perturbed FRW metric and Newtonian cosmology

Syksy Rasanen

Cosmology and Nongalactic Astrophysics · Submitted 25 Feb 2010

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

The authors' main claim We discuss why the arguments based on the linear theory are not valid.

how it is stated · asserted 0.90 read the record →

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.70 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of non-linear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasise the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of non-linear density perturbations.	background 1.00	0.04	0.08	asserted 0.91
s1	We discuss why the arguments based on the linear theory are not valid.	contribution 0.99	0.78	0.22	asserted 0.90
s2	We emphasise the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.	contribution 0.95	0.71	0.11	asserted 0.77

What kind of paper the classifier reports this is: position or commentary 1.00 · evidence from argument 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

It has been argued that the effect of cosmological structure formation on the average expansion rate is negligible, because the linear approximation to the metric remains applicable in the regime of non-linear density perturbations. We discuss why the arguments based on the linear theory are not valid. We emphasise the difference between Newtonian gravity and the weak field, small velocity limit of general relativity in the cosmological setting.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A new framework for analyzing the effects of small scale inhomogeneities in cosmology
gr-qc 2010-11 accept novelty 7.0 of 10

Within a rigorously defined shortwave framework, small-scale matter inhomogeneities cannot mimic dark energy; their only background effect is a traceless, positive-energy effective stress tensor.
Newtonian and Relativistic Cosmologies
gr-qc 2011-11 conditional novelty 6.0 of 10

An explicit dictionary maps Newtonian dust cosmologies to general relativistic spacetimes, and the size of the correction terms needed to satisfy Einstein's equation becomes a computable test of when Newtonian simulat...
Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?
gr-qc 2015-05 conditional novelty 5.0 of 10

Green and Wald's no-go result on cosmological backreaction requires unstated extra assumptions; without them the claimed trace-free backreaction term vanishes, so the irrelevance claim is unproven.
Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology
astro-ph.CO 2011-09 accept novelty 3.0 of 10

The paper concludes that cosmological backreaction from averaging over structure is not safely negligible for precision cosmology, although its size on the largest scales remains unsettled.
Backreaction in late-time cosmology
astro-ph.CO 2011-12 accept novelty 2.0 of 10

Backreaction from nonlinear structure formation is a physically real effect in general relativity that might, but has not been shown to, replace dark energy.

How the literature uses it

18 arXiv papers cite this in 35 sentences

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 citing it · 31 sentences without a confident label

Cites it as support 1 paper

However, when density perturbations become nonlinear, contributions from higher order terms become as important as the second order terms [ref] .

Backreaction in late-time cosmology · Perturbative arguments · 0.96

Cites it as background 3 papers

The second question has been studied in many papers with regard to the average expansion rate [ref] (see [ref] for further discussion and references).

Light propagation and the average expansion rate in near-FRW universes · Introduction · 0.96
There has been much discussion about the possible gauge-dependence of the average expansion rate [ref] .

Backreaction in late-time cosmology · The average expansion rate · 0.95
An unresolved issue in cosmology is the effect of the structure formation on the cosmological observations beyond perturbative analysis of the Friedmann-Robertson-Walker or FRW models [ref] .

On the role of shear in cosmological averaging · Introduction · 0.99

What it cites · 151 sentences without a confident label

Contests 10 papers

However, this is not the case: for a metric of the form metric, the velocity $u^i$ (and thus also $θ$) expanded as a series in $Φ$ necessarily contains an infinite (or zero) number of spatial derivatives [ref] .

Dark energy from backreaction · The perturbative calculation · contest 0.80
The effect of backreaction cannot be described merely as a change in the FRW background [ref] , unlike argued in [ref] .

Light propagation in statistically homogeneous and isotropic dust universes · The perturbative calculation · contest 0.75
The effect of backreaction cannot be described merely as a change in the FRW background [ref] , unlike argued in [ref] .

Cosmological background solutions and cosmological backreactions · The perturbative calculation · contest 0.75

Cites as support 16 papers

Analysis of the Newtonian theory in this case would be misleading, because the Newtonian solutions betray no sign of the fact that starting from general relativity, they do not exist, even at small velocities and weak fields[This underlines that it is not sufficient to look at the Newtonian limit of the equations of general relativity, but it is necessary to consider the limit of solutions, because in general the operations of taking the limit and solving the equations do not commute [ref] .].

Theorems on shear-free perfect fluids with their Newtonian analogues · The Newtonian limit · 0.99
The variance of the expansion rate and the shear combine to give a total derivative, so $$ reduces to a boundary term [ref] .

Averaging inhomogeneous Newtonian cosmologies · The Newtonian limit · 0.98
And at second order, the metric cannot be written in the simple diagonal form metric [ref] .

Relativistic second-order perturbations of the Einstein-de Sitter Universe · The perturbative calculation · 0.98

Cites as background 12 papers

It has been proposed that the observed increase in the expansion rate and the distance scale of the universe at late times relative to the matter-dominated homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model could be explained by the breakdown of the homogeneous and isotropic approximation because of the formation of non-linear structures [ref] .

Accelerated expansion without dark energy · Introduction · 0.80
It has been proposed that the observed increase in the expansion rate and the distance scale of the universe at late times relative to the matter-dominated homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model could be explained by the breakdown of the homogeneous and isotropic approximation because of the formation of non-linear structures [ref] .

On average properties of inhomogeneous cosmologies · Introduction · 0.80
It has been proposed that the observed increase in the expansion rate and the distance scale of the universe at late times relative to the matter-dominated homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model could be explained by the breakdown of the homogeneous and isotropic approximation because of the formation of non-linear structures [ref] .

Dark energy from backreaction · Introduction · 0.80

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