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Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe

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Norimasa Sugiura, Ken-ichi Nakao, Tomohiro Harada

General Relativity and Quantum Cosmology · Submitted 24 Nov 1999

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

The authors' main claim We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/9911090 (version 1)
Pith IDA5V4XLG3, Pith's permanent record of this paper and its review
CitationKen-ichi Nakao, Norimasa Sugiura, Tomohiro Harada. "Distance-redshift relation in an isotropic inhomogeneous universe II: Spherically symmetric dust-shell universe." arXiv:gr-qc/9911090 (1999). https://pith.science/paper/A5V4XLG3
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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, 4,330 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the distance-redshift relation, we discuss an impact of the local inhomogeneities on determination of the cosmological parameters through the observation of the locally inhomogeneous universe.

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 The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. contribution 0.92 0.78 0.04 asserted 0.78
s1 We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. result 1.00 0.94 0.67 asserted 1.00
s2 This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. interpretation 1.00 0.30 0.57 hedged possibility 0.85
s3 We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. contribution 0.99 0.85 0.03 asserted 0.80
s4 Combining this with the results of the distance-redshift relation, we discuss an impact of the local inhomogeneities on determination of the cosmological parameters through the observation of the locally inhomogeneous universe. contribution 0.77 0.81 0.13 unclear 0.63

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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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

The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitationally bound objects. Combining this with the results of the distance-redshift relation, we discuss an impact of the local inhomogeneities on determination of the cosmological parameters through the observation of the locally inhomogeneous universe.

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