Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions
Abstract
We investigate the Wightman function, the vacuum expectation values of the field squared, and the energy-momentum tensor for a scalar field with a general curvature coupling parameter in (D+1)-dimensional de Sitter (dS) spacetime with an arbitrary number of compactified spatial dimensions. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. Recurrence formulas are derived which express the vacuum expectation values for the dS spacetime of topology R{sup p}x(S{sup 1}){sup q} in the form of the sum of the vacuum expectation values in the topology R{sup p+1}x(S{sup 1}){sup q-1} and the part induced by the compactness of the (p+1)th spatial dimension. The behavior of the topological parts is investigated in various asymptotic regions of the parameters. In the early stages of the cosmological evolution, the topological parts dominate the contribution in the expectation values due to the uncompactified dS part. In this limit the behavior of the topological parts does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion, the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatorymore »
- Authors:
-
- INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy)
- Department of Physics, Yerevan State University, 1 Alex Manoogian Street, 0025 Yerevan (Armenia)
- Publication Date:
- OSTI Identifier:
- 21205183
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. D, Particles Fields
- Additional Journal Information:
- Journal Volume: 77; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.77.124010; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASYMPTOTIC SOLUTIONS; COMPACTIFICATION; COUPLING; DE SITTER GROUP; DENSITY; ENERGY-MOMENTUM TENSOR; EVOLUTION; EXPANSION; MANY-DIMENSIONAL CALCULATIONS; MASS; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; SCALAR FIELDS; SPACE-TIME; WIGHTMAN FIELD THEORY
Citation Formats
Bellucci, S, and Saharian, A A. Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions. United States: N. p., 2008.
Web. doi:10.1103/PHYSREVD.77.124010.
Bellucci, S, & Saharian, A A. Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions. United States. https://doi.org/10.1103/PHYSREVD.77.124010
Bellucci, S, and Saharian, A A. 2008.
"Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions". United States. https://doi.org/10.1103/PHYSREVD.77.124010.
@article{osti_21205183,
title = {Wightman function and vacuum densities in de Sitter spacetime with toroidally compactified dimensions},
author = {Bellucci, S and Saharian, A A},
abstractNote = {We investigate the Wightman function, the vacuum expectation values of the field squared, and the energy-momentum tensor for a scalar field with a general curvature coupling parameter in (D+1)-dimensional de Sitter (dS) spacetime with an arbitrary number of compactified spatial dimensions. Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. Recurrence formulas are derived which express the vacuum expectation values for the dS spacetime of topology R{sup p}x(S{sup 1}){sup q} in the form of the sum of the vacuum expectation values in the topology R{sup p+1}x(S{sup 1}){sup q-1} and the part induced by the compactness of the (p+1)th spatial dimension. The behavior of the topological parts is investigated in various asymptotic regions of the parameters. In the early stages of the cosmological evolution, the topological parts dominate the contribution in the expectation values due to the uncompactified dS part. In this limit the behavior of the topological parts does not depend on the curvature coupling parameter and coincides with that for a conformally coupled massless field. At late stages of the cosmological expansion, the expectation values are dominated by the part corresponding to uncompactified dS spacetime. The vanishing of the topological parts is monotonic or oscillatory in dependence of the mass and the curvature coupling parameter of the field.},
doi = {10.1103/PHYSREVD.77.124010},
url = {https://www.osti.gov/biblio/21205183},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 77,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2008},
month = {Sun Jun 15 00:00:00 EDT 2008}
}