Inflation in a closed universe

Ratra, Bharat

doi:10.1103/physrevd.96.103534

Inflation in a closed universe

Journal Article · Tue Nov 21 23:00:00 EST 2017 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.96.103534· OSTI ID:1511831

Ratra, Bharat ^[1]

Kansas State Univ., Manhattan, KS (United States); Kansas State University

To derive a power spectrum for energy density inhomogeneities in a closed universe, we investigate a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and nonrelativistic matter epochs. (For our usage it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking’s prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wave number in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

View Accepted Manuscript (DOE)

Research Organization:: Kansas State Univ., Manhattan, KS (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0011840

OSTI ID:: 1511831

Alternate ID(s):: OSTI ID: 1409869

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 10 Vol. 96; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Quintessence with a constant equation of state in hyperbolic universes Aurich, R.; Steiner, F. arXiv https://doi.org/10.48550/arxiv.astro-ph/0212471	text	January 2002
Cosmic Degeneracy with Dark Energy Equation of State Crooks, James L.; Dunn, James O.; Frampton, Paul H. arXiv https://doi.org/10.48550/arxiv.astro-ph/0305495	text	January 2003
Non-Gaussian Error Distribution of Hubble Constant Measurements Chen, Gang; Gott, J. Richard; Ratra, Bharat arXiv https://doi.org/10.48550/arxiv.astro-ph/0308099	text	January 2003
Implication of Dark Energy Parametrizations on the Determination of the Curvature of the Universe Ichikawa, Kazuhide; Kawasaki, Masahiro; Sekiguchi, Toyokazu arXiv https://doi.org/10.48550/arxiv.astro-ph/0605481	text	January 2006
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Why Not Consider Closed Universes? White, Martin; Scott, Douglas arXiv https://doi.org/10.48550/arxiv.astro-ph/9508157	text	January 1995
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