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Cited by 714Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical Physics

Formalizing the slow-roll approximation in inflation

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Liddle, Andrew R., Parsons, Paul, Barrow, John D.·1994·Physical Review D
DOI 10.1103/physrevd.50.7222
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Abstract

The meaning of the inflationary slow-roll approximation is formalized. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the evolution of the potential energy density. The vital role of the inflationary attractor solution is emphasized, and some of its properties described. We propose a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual e-foldings of physical expansion, and derive relevant formulas. We introduce an infinite hierarchy of slow-roll parameters, and show that only a finite number of them are required to produce results to a given order. The extension of the slow-roll approximation into an analytic slow-roll expansion, converging on the exact solution, is provided. Its role in calculations of inflationary dynamics is discussed. We explore rational approximants as a method of extending the range of convergence of the slow-roll expansion up to, and beyond, the end of inflation.

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Crossref · 10.1103/physrevd.50.7222

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  • The agreement between the WMAP results and the most recent analysis of the primordial deuterium abundance yields a value of the baryon asymmetry.

    “The agreement between the WMAP results[15, 16, 17, 18] and the most recent analysis of the primordial deuterium abundance[46] yields”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [46]

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Related

Authors
Liddle, A. R., Parsons, P., & Barrow, J. D.
Affiliations
University of Sussex (GB)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1994-12-15
Volume
50
Issue
12
Pages
7222-7232
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.50.7222
OpenAlex
W2067502036
Cited by
714
References
21
Citations by year
2026: 28 · 2025: 40 · 2024: 48 · 2023: 34 · 2022: 33 · 2021: 30 · 2020: 41 · 2019: 36 · 2018: 39 · 2017: 45 · 2016: 35 · 2015: 39 · 2014: 19 · 2013: 16 · 2012: 15
FWCI
11.74
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
slow-roll approximation, cosmic inflation, Hamilton-Jacobi equation, Hubble parameter evolution, inflationary attractors, slow-roll parameters, rational approximants, end of inflation, scalar field potential

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