Nonlinear evolution of long-wavelength metric fluctuations in inflationary models

Journal Article · Sat Dec 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.3936· OSTI ID:5918080

Salopek, D S ^[1]; Bond, J R ^[2]

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1. NASA/Fermilab Astrophysics Center, Batavia, IL (USA)
2. Canadian Institute for Advanced Research Program, Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto (Canada)

Stochastic inflation can be viewed as a sequence of two-step processes. In the first step a stochastic impulse from short-distance quantum fluctuations acts on long waves---the interaction. In the second step the long waves evolve semiclassically---the propagation. Both steps must be developed to address whether fluctuations for cosmic structure formation may be non-Gaussian. We describe a formalism for following the nonlinear propagation of long-wavelength metric and scalar-field fluctuations. We perform an expansion in spatial gradients of the Arnowitt-Deser-Misner equations and we retain only terms up to first order. At each point the fields obey evolution equations like those in a homogeneous universe, but now described by a local scale factor {ital e}{sup {alpha}} and Hubble expansion rate {ital H}. However, the different points are joined together through the momentum constraint equation. The gradient expansion is appropriate for inflation if the long-wave fields are smoothed over scales below {ital e}{sup {minus}{alpha}}{ital H}{sup {minus}1}. Our equations are naturally described in the Einstein-Hamilton-Jacobi framework, which governs an ensemble of inhomogeneous universes, and which may be interpreted as a semiclassical approximation to the quantum theory.

• OSTI ID: 5918080
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:12; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COSMOLOGICAL MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
GRAVITATIONAL FIELDS
GREEN FUNCTION
HAMILTON-JACOBI EQUATIONS
HUBBLE EFFECT
INFLATIONARY UNIVERSE
MATHEMATICAL MODELS
MECHANICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM MECHANICS
SCALAR FIELDS
SEMICLASSICAL APPROXIMATION
SPACE-TIME
STOCHASTIC PROCESSES
WAVE FUNCTIONS