Scalar field in the anisotropic universe

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.083517· OSTI ID:21409573

Kim, Hyeong-Chan ^[1]; Minamitsuji, Masato ^[2]

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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)

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.

• OSTI ID: 21409573
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.083517; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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