Cosmology and Nongalactic Astrophysics · arXiv:1012.0784 v1 · submitted 3 Dec 2010
Backreaction as an alternative to dark energy and modified gravity
The paper says
“We review how inhomogeneities affect the average expansion rate and can lead to acceleration, and consider a semi-realistic model where the observed timescale of ten billion years emerges from structure formation.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
The predictions of homogeneous and isotropic cosmological models with ordinary matter and gravity are off by a factor of two in the late universe. One possible explanation is the known breakdown of homogeneity and isotropy due to the formation of non-linear structures. We review how inhomogeneities affect the average expansion rate and can lead to acceleration, and consider a semi-realistic model where the observed timescale of ten billion years emerges from structure formation. We also discuss the relation between the average expansion rate and observed quantities.
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.
abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: hedged possibility 0.55
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.82 · compares with prior results 0.44 · 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.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| The predictions of homogeneous and isotropic cosmological models with ordinary matter and gravity are off by a factor of two in the late universe. | background 0.98 | 0.12 | 0.06 | asserted 1.00 |
| One possible explanation is the known breakdown of homogeneity and isotropy due to the formation of non-linear structures. | background 0.96 | 0.05 | 0.08 | hedged possibility 0.96 |
| We review how inhomogeneities affect the average expansion rate and can lead to acceleration, and consider a semi-realistic model where the observed timescale of ten billion years emerges from structure formation. | contribution 0.98 | 0.71 | 0.60 | hedged possibility 0.55 |
| We also discuss the relation between the average expansion rate and observed quantities. | contribution 0.99 | 0.60 | 0.04 | unclear 0.84 |
What kind of paper the classifier reports this is: review 0.99 · evidence from literature 0.59
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
Not run
- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,548 input tokens, $0.0001 reported.
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
Cited by 2 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Average expansion rate and light propagation in a cosmological Tardis spacetime astro-ph.CO · Aug 2013
- Backreaction: directions of progress astro-ph.CO · Feb 2011
How the literature uses it
10 arXiv papers cite this in 16 sentences
Papers citing it · 8 sentences without a confident label
Cites it as support 1 paper
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As a result, average acceleration may not be needed to explain the observations [ref] .
Average expansion rate and light propagation in a cosmological Tardis spacetime · Signatures of backreaction · 0.96
Cites it as background 7 papers
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The effect of deviations from homogeneity and isotropy on average quantities (in particular, the average expansion rate) is called backreaction [ref] .
Backreaction: directions of progress · Three choices for a factor of two · 0.83
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The effect of deviations from homogeneity and/or isotropy on the average expansion rate is known as backreaction [ref] (see [ref] for reviews).
Violation of the FRW consistency condition as a signature of backreaction · Introduction · 0.98
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This feature of general relativity is known as backreaction [ref] ; see [ref] for reviews.
Average expansion rate and light propagation in a cosmological Tardis spacetime · Introduction · 0.95
What it cites · 36 sentences without a confident label
Uses the method or tool of 2 papers
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Averaging Rayloc–consloc, we obtain the Buchert equations [ref] 3 /a = - 4 πρ + 3 = 8 πρ - 1/2 - 1/2 _t ρ + 3 /a ρ = 0 ,
On average properties of inhomogeneous fluids in general relativity I: dust cosmologies · The average expansion rate · 0.86
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The BBKS transfer function [ref] is a fit to numerical calculations (we take a baryon fraction of $0.2$), and the BDG form introduced in [ref] is a simple analytically tractable function with the correct qualitative features.
Fluctuations of the luminosity distance · A statistical semi-realistic model · 0.81
Uses data or values from 1 paper
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The matter-radiation equality scale is $^-1≈13.7^-1$ Mpc $≈$ 100 Mpc, using the value $=0.14$ [ref] .
Model-independent cosmological constraints from the CMB · A statistical semi-realistic model · 0.98
Cites as support 5 papers
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Since the evolution of structures is governed by the proper time, one can argue that this is close to the hypersurface of statistical homogeneity and isotropy [ref] .
Evaluating backreaction with the peak model of structure formation · The redshift · 0.99
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Since the evolution of structures is governed by the proper time, one can argue that this is close to the hypersurface of statistical homogeneity and isotropy [ref] .
Light propagation in statistically homogeneous and isotropic dust universes · The redshift · 0.99
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Since the evolution of structures is governed by the proper time, one can argue that this is close to the hypersurface of statistical homogeneity and isotropy [ref] .
Accelerated expansion from structure formation · The redshift · 0.99
Cites as background 3 papers
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The equations Ray–cons were first derived by Thomas Buchert in 1999 [ref] .
On average properties of inhomogeneous fluids in general relativity I: dust cosmologies · The average expansion rate · 0.94
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(For discussion of vorticity and non-dust terms in the energy-momentum tensor, see [ref] .)
Light propagation in statistically homogeneous and isotropic universes with general matter content · A two-region toy model · 0.95
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(For discussion of vorticity and non-dust terms in the energy-momentum tensor, see [ref] .)
On average properties of inhomogeneous fluids in general relativity II: perfect fluid cosmologies · A two-region toy model · 0.95
Challenges and discussion
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