Stochastic inflation: Quantum phase-space approach

Journal Article · Tue Sep 15 00:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.2408· OSTI ID:7173916

Habib, S ^[1]

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1. Department of Physics, The University of British Columbia, 6224 Agriculture Road, Vancouver, British Columbia, V6T1Z1 (Canada) T-6, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to {l angle}{Phi}{sup 2}{r angle}). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does {ital not} by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence.

• OSTI ID: 7173916
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 46:6; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
INFLATIONARY UNIVERSE
QUANTUM FIELD THEORY
STOCHASTIC PROCESSES
BOLTZMANN-VLASOV EQUATION
DISTRIBUTION FUNCTIONS
HUBBLE EFFECT
INFRARED DIVERGENCES
PHASE SPACE
QUANTUM MECHANICS
SCALAR FIELDS
SPACE-TIME
THERMODYNAMIC PROPERTIES
WIGNER THEORY
COSMOLOGICAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SPACE
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)