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Asymptotics of linearized cosmological perturbations

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Paul T. Allen, Alan D. Rendall

Analysis of PDEs · Submitted 14 Jun 2009

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

The authors' main claim This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times.

how it is stated · asserted 1.00 read the record →

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arXiv ID0906.2517 (version 1)
Pith IDU5YIZDDO, Pith's permanent record of this paper and its review
CitationAlan D. Rendall, Paul T. Allen. "Asymptotics of linearized cosmological perturbations." arXiv:0906.2517 (2009). https://pith.science/paper/U5YIZDDO
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The compiled record

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. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,877 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.25 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state it is found that the late-time asymptotic behaviour is qualitatively different from that in the linear case.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. background 1.00 0.05 0.02 asserted 1.00
s1 This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times. contribution 0.96 0.96 0.50 asserted 1.00
s2 The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. method 0.55 0.31 0.04 asserted 1.00
s3 Expansions for the solutions are obtained in both asymptotic regimes. result 0.50 0.95 0.12 asserted 0.99
s4 In both cases it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. result 0.96 0.93 0.29 asserted 1.00
s5 For some nonlinear equations of state it is found that the late-time asymptotic behaviour is qualitatively different from that in the linear case. result 1.00 0.92 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state it is found that the late-time asymptotic behaviour is qualitatively different from that in the linear case.

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