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Title: Scalar field in the anisotropic universe

Abstract

We discuss the primordial spectrum of a massless and minimally coupled scalar field, produced during the initial anisotropic epoch before the onset of inflation. We consider two models of the anisotropic cosmology, the (planar) Kasner-de Sitter solution (Bianchi I) and the Taub-NUT-de Sitter solution (Bianchi IX), where the 3-space geometry is initially anisotropic, followed by the de Sitter phase due to the presence of a positive cosmological constant. We discuss the behavior of a quantized, massless and minimally coupled scalar field in the anisotropic stage. This scalar field is not the inflaton and hence does not contribute to the background dynamics. We focus on the quantization procedure and evolution in the preinflationary anisotropic background. Also, in this paper for simplicity the metric perturbations are not taken into account. The initial condition is set by the requirement that the scalar field is initially in an adiabatic state. Usually, in a quantum harmonic oscillator system, an adiabatic process implies the one where the potential changes slowly enough compared to its size, and the time evolution can be obtained from the zeroth order WKB approximation. In our case, such a vacuum state exists only for limited solutions of the anisotropic universe, whose spacetimemore » structure is regular in the initial times. In this paper, we call our adiabatic vacuum state the anisotropic vacuum. In the Kasner-de Sitter model, for one branch of planar solutions there is an anisotropic vacuum unless k{sub 3{ne}}0, where k{sub 3} is the comoving momentum along the third direction, while in the other branch there is no anisotropic vacuum state. In the first branch, for the moderate modes, k{sub 3{approx}}k, where k is the total comoving momentum, the scalar power spectrum has an oscillatory behavior and its direction dependence is suppressed. For the planar modes, k{sub 3}<<k, in contrast, the direction dependence becomes more important, because of the amplification of the scalar amplitude during this interval of the violation of WKB approximation in the initial anisotropic stage. The qualitative behaviors in the Taub-NUT-de Sitter models are very similar to the case of the first branch of the planar Kasner-de Sitter model.« less

Authors:
 [1];  [2]
  1. Division of Liberal Arts, Chungju National University, Chungju 380-702 (Korea, Republic of)
  2. Center for Quantum Spacetime, Sogang University, Shinsu-dong 1, Mapo-gu, Seoul, 121-742 (Korea, Republic of)
Publication Date:
OSTI Identifier:
21409573
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.81.083517; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ADIABATIC PROCESSES; ANISOTROPY; COSMOLOGICAL CONSTANT; COSMOLOGY; DE SITTER SPACE; DISTURBANCES; HARMONIC OSCILLATORS; MATHEMATICAL SOLUTIONS; METRICS; PERTURBATION THEORY; QUANTIZATION; SCALAR FIELDS; SIMULATION; SPACE-TIME; SPECTRA; UNIVERSE; VACUUM STATES; WKB APPROXIMATION; APPROXIMATIONS; CALCULATION METHODS; MATHEMATICAL SPACE; SPACE

Citation Formats

Kim, Hyeong-Chan, and Minamitsuji, Masato. Scalar field in the anisotropic universe. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.083517.
Kim, Hyeong-Chan, & Minamitsuji, Masato. Scalar field in the anisotropic universe. United States. https://doi.org/10.1103/PHYSREVD.81.083517
Kim, Hyeong-Chan, and Minamitsuji, Masato. 2010. "Scalar field in the anisotropic universe". United States. https://doi.org/10.1103/PHYSREVD.81.083517.
@article{osti_21409573,
title = {Scalar field in the anisotropic universe},
author = {Kim, Hyeong-Chan and Minamitsuji, Masato},
abstractNote = {We discuss the primordial spectrum of a massless and minimally coupled scalar field, produced during the initial anisotropic epoch before the onset of inflation. We consider two models of the anisotropic cosmology, the (planar) Kasner-de Sitter solution (Bianchi I) and the Taub-NUT-de Sitter solution (Bianchi IX), where the 3-space geometry is initially anisotropic, followed by the de Sitter phase due to the presence of a positive cosmological constant. We discuss the behavior of a quantized, massless and minimally coupled scalar field in the anisotropic stage. This scalar field is not the inflaton and hence does not contribute to the background dynamics. We focus on the quantization procedure and evolution in the preinflationary anisotropic background. Also, in this paper for simplicity the metric perturbations are not taken into account. The initial condition is set by the requirement that the scalar field is initially in an adiabatic state. Usually, in a quantum harmonic oscillator system, an adiabatic process implies the one where the potential changes slowly enough compared to its size, and the time evolution can be obtained from the zeroth order WKB approximation. In our case, such a vacuum state exists only for limited solutions of the anisotropic universe, whose spacetime structure is regular in the initial times. In this paper, we call our adiabatic vacuum state the anisotropic vacuum. In the Kasner-de Sitter model, for one branch of planar solutions there is an anisotropic vacuum unless k{sub 3{ne}}0, where k{sub 3} is the comoving momentum along the third direction, while in the other branch there is no anisotropic vacuum state. In the first branch, for the moderate modes, k{sub 3{approx}}k, where k is the total comoving momentum, the scalar power spectrum has an oscillatory behavior and its direction dependence is suppressed. For the planar modes, k{sub 3}<<k, in contrast, the direction dependence becomes more important, because of the amplification of the scalar amplitude during this interval of the violation of WKB approximation in the initial anisotropic stage. The qualitative behaviors in the Taub-NUT-de Sitter models are very similar to the case of the first branch of the planar Kasner-de Sitter model.},
doi = {10.1103/PHYSREVD.81.083517},
url = {https://www.osti.gov/biblio/21409573}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 81,
place = {United States},
year = {Thu Apr 15 00:00:00 EDT 2010},
month = {Thu Apr 15 00:00:00 EDT 2010}
}