Inflation in a closed universe
Abstract
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 spectrummore »
- Authors:
-
- Kansas State Univ., Manhattan, KS (United States)
- Publication Date:
- Research Org.:
- Kansas State Univ., Manhattan, KS (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1511831
- Alternate Identifier(s):
- OSTI ID: 1409869
- Grant/Contract Number:
- SC0011840; SC001184
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 10; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
Ratra, Bharat. Inflation in a closed universe. United States: N. p., 2017.
Web. doi:10.1103/physrevd.96.103534.
Ratra, Bharat. Inflation in a closed universe. United States. https://doi.org/10.1103/physrevd.96.103534
Ratra, Bharat. 2017.
"Inflation in a closed universe". United States. https://doi.org/10.1103/physrevd.96.103534. https://www.osti.gov/servlets/purl/1511831.
@article{osti_1511831,
title = {Inflation in a closed universe},
author = {Ratra, Bharat},
abstractNote = {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.},
doi = {10.1103/physrevd.96.103534},
url = {https://www.osti.gov/biblio/1511831},
journal = {Physical Review. D.},
issn = {2470-0010},
number = 10,
volume = 96,
place = {United States},
year = {Wed Nov 22 00:00:00 EST 2017},
month = {Wed Nov 22 00:00:00 EST 2017}
}
Web of Science
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