Pith. Sign in

RECORD

Wave functions for arbitrary operator ordering in the de Sitter minisuperspace approximation

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
D.L. Wiltshire

General Relativity and Quantum Cosmology · Submitted 24 May 1999

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

The authors' main claim The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDgr-qc/9905090 (version 1)
Pith ID2X7BN7OE, Pith's permanent record of this paper and its review
CitationD.L. Wiltshire. "Wave functions for arbitrary operator ordering in the de Sitter minisuperspace approximation." arXiv:gr-qc/9905090 (1999). https://pith.science/paper/2X7BN7OE
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,104 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We derive exact series solutions for the Wheeler-DeWitt equation corresponding to a spatially closed Friedmann-Robertson-Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The resulting wave functions are those relevant to the approximation which has been widely used in two-dimensional minisuperspace models with an inflationary scalar field for the purpose of predicting the period of inflation which results from competing boundary condition proposals for the wave function of the universe. The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included.

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 We derive exact series solutions for the Wheeler-DeWitt equation corresponding to a spatially closed Friedmann-Robertson-Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. contribution 0.96 0.97 0.40 asserted 1.00
s1 The resulting wave functions are those relevant to the approximation which has been widely used in two-dimensional minisuperspace models with an inflationary scalar field for the purpose of predicting the period of inflation which results from competing boundary condition proposals for the wave function of the universe. interpretation 0.54 0.39 0.12 asserted 1.00
s2 The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included. result 0.99 0.85 0.44 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

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

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

We derive exact series solutions for the Wheeler-DeWitt equation corresponding to a spatially closed Friedmann-Robertson-Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The resulting wave functions are those relevant to the approximation which has been widely used in two-dimensional minisuperspace models with an inflationary scalar field for the purpose of predicting the period of inflation which results from competing boundary condition proposals for the wave function of the universe. The problem that Vilenkin's tunneling wave function is not normalizable for general operator orderings, is shown to persist for other values of the spatial curvature, and when additional matter degrees of freedom such as radiation are included.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.