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Nonequilibrium corrections to energy spectra of massive particles in expanding universe

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A.D. Dolgov

High Energy Physics - Phenomenology · Submitted 7 Jun 1996

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

The authors' main claim Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-ph/9606266 (version 1)
Pith IDQY4Z7K7C, Pith's permanent record of this paper and its review
CitationA.D. Dolgov. "Nonequilibrium corrections to energy spectra of massive particles in expanding universe." arXiv:hep-ph/9606266 (1996). https://pith.science/paper/QY4Z7K7C
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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, 4,919 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.68 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.64 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. For the case of an energy independent amplitude of elastic scattering, an exact partial differential equation is derived instead of the usual integro-differential one. A simple perturbative solution of the former is found. For the case of an energy-dependent amplitude the problem cannot be reduced to the differential equation but the solution of the original integro-differential equation can be found in terms of the Taylor expansion, which in the case of aconstant amplitude shows a perfect agreement with the perturbative solution of the differential equation. Corrections to the spectrum of (possibly) massive tau-neutrinos are calculated. The method may be of more general interest and can be applied to the calculation of spectrum distortion in other (not necessarily cosmological) nonequilibrium processes.

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 Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. contribution 0.95 0.92 0.41 asserted 1.00
s1 For the case of an energy independent amplitude of elastic scattering, an exact partial differential equation is derived instead of the usual integro-differential one. method 0.74 0.94 0.09 asserted 1.00
s2 A simple perturbative solution of the former is found. method 0.78 0.93 0.08 asserted 1.00
s3 For the case of an energy-dependent amplitude the problem cannot be reduced to the differential equation but the solution of the original integro-differential equation can be found in terms of the Taylor expansion, which in the case of aconstant amplitude shows a perfect agreement with the perturbative solution of the differential equation. method 0.75 0.93 0.16 asserted 1.00
s4 Corrections to the spectrum of (possibly) massive tau-neutrinos are calculated. result 0.82 0.93 0.28 asserted 0.91
s5 The method may be of more general interest and can be applied to the calculation of spectrum distortion in other (not necessarily cosmological) nonequilibrium processes. interpretation 0.64 0.23 0.11 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • 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

Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. For the case of an energy independent amplitude of elastic scattering, an exact partial differential equation is derived instead of the usual integro-differential one. A simple perturbative solution of the former is found. For the case of an energy-dependent amplitude the problem cannot be reduced to the differential equation but the solution of the original integro-differential equation can be found in terms of the Taylor expansion, which in the case of aconstant amplitude shows a perfect agreement with the perturbative solution of the differential equation. Corrections to the spectrum of (possibly) massive tau-neutrinos are calculated. The method may be of more general interest and can be applied to the calculation of spectrum distortion in other (not necessarily cosmological) nonequilibrium processes.

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