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Gravitational Waves From the End of Inflation: Computational Strategies

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Richard Easther, John T. Giblin Jr, Eugene A. Lim

Astrophysics · Submitted 18 Dec 2007

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

The authors' main claim These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation.

how it is stated · asserted 1.00 read the record →

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arXiv ID0712.2991 (version 1)
Pith IDP5PXKPTA, Pith's permanent record of this paper and its review
CitationEugene A. Lim, John T. Giblin Jr, Richard Easther. "Gravitational Waves From the End of Inflation: Computational Strategies." arXiv:0712.2991 (2007). https://pith.science/paper/P5PXKPTA
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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, 4,895 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.77 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. We explicitly calculate this spectrum for both quartic and quadratic models of chaotic inflation, and low-scale hybrid models. In particular, we consider hybrid models with an ``inverted'' potential. These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation.

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 Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. background 1.00 0.05 0.03 hedged possibility 0.99
s1 This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. background 0.99 0.07 0.09 hedged possibility 0.99
s2 Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. contribution 0.81 0.95 0.16 asserted 1.00
s3 We explicitly calculate this spectrum for both quartic and quadratic models of chaotic inflation, and low-scale hybrid models. contribution 0.87 0.96 0.10 asserted 1.00
s4 In particular, we consider hybrid models with an ``inverted'' potential. contribution 0.86 0.50 0.05 asserted 0.97
s5 These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation. result 0.94 0.95 0.47 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.86 · evidence from simulation or computation 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

Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. We explicitly calculate this spectrum for both quartic and quadratic models of chaotic inflation, and low-scale hybrid models. In particular, we consider hybrid models with an ``inverted'' potential. These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation.

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References
How later papers used it

49 later papers cite it

Evidence: substantial. 27 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 74 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 5 of 11 papers with this label · 5 by the same authors

By the same authors

  • Invoked Parseval's theorem, citing this paper, to rewrite its gravitational wave energy density expression.

    Gravitational Waves from Global Second Order Phase Transitions (2011) (same authors) · 0.91 · paraphrased: the licence does not allow quoting

  • Computed the transverse-traceless part of the first order perturbative metric using the method described in this paper, evolving Fourier modes in Fourier space with a fourth-order-in-time Runge-Kutta scheme.

    Gravitational Waves from Oscillon Preheating (2013) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

  • Computed gravitational waves by solving the sourced, inhomogeneous linear partial differential equation for the transverse-traceless part of the metric in momentum space, similar to the implementation in this paper.

    Gravitational waves from gauge preheating (2018) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

  • Calculated the power in gravitational waves by passively calculating tensor perturbations of the metric, following the basic procedure of this paper.

    Gravitational Waves from Kinetic Preheating (2024) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

  • Computed the gravitational wave spectrum passively, citing this paper, by calculating the transverse-traceless parts of the matter stress tensor.

    Gauge preheating with full general relativity (2023) (same authors) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

47 arXiv papers cite this in 72 sentences

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

Papers citing it · 35 sentences without a confident label

Builds on it 1 paper
  • Because fields decay throughout inflation, we expect an additional gravitational wave spectrum resulting from the superposition of spectra similar to the ones found in [ref] ; since the process operates within the horizon, the peaks of the spectra are always generated at the same fraction of the Hubble radius whenever a field decays.

    Multi-Field Inflation on the Landscape · Outlook · 0.84

Uses its method or tool 11 papers
Compares with it 2 papers
  • While the detailed mechanism is different, this signal has much in common with the gravitational wave background that can be generated during preheating or parametric resonance [ref] .

    Thermal Inflation and the Gravitational Wave Background · Discussion · 0.96

  • We note that lattice studies of GW production from preheating with quartic inflaton potentials have a long history [ref] , and our results for the spectator-sourced signal are qualitatively consistent with the enhanced amplitudes found in those works for the inflaton-sourced case.

    Gravitational Waves from Matter Perturbations of Spectator Scalar Fields · Gravitational Waves with Quartic Inflaton Potential · 0.96

Cites it as support 1 paper
Cites it as background 19 papers

What it cites · 42 sentences without a confident label

Uses the method or tool of 2 papers
Uses data or values from 3 papers
Compares with 7 papers
  • The box method (as implemented in [ref] ) yields spectra with a significantly higher amplitude than those found with the spectral or Green's function methods, but that the latter methods agree very closely with each other.

    Stochastic Gravitational Wave Production After Inflation · Introduction · 0.92

  • In addition to the previous work of the current authors [ref] , two other independent codes have been recently been developed to address this problem [ref] and we explicitly compare the results of our spectral algorithm that the Green's function algorithm of [ref] , showing that the difference between the computed spectra is of the same order as that introduced by the finite resolution of the underlying spatial lattice.

    Gravitational Wave Production At The End Of Inflation · Discussion · 0.98

  • In addition to the previous work of the current authors [ref] , two other independent codes have been recently been developed to address this problem [ref] and we explicitly compare the results of our spectral algorithm that the Green's function algorithm of [ref] , showing that the difference between the computed spectra is of the same order as that introduced by the finite resolution of the underlying spatial lattice.

    A Gravitational Wave Background from Reheating after Hybrid Inflation · Discussion · 0.98

Cites as background 14 papers

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