Stochastic inflation and nonlinear gravity

Journal Article · Fri Feb 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.1005· OSTI ID:5716832

Salopek, D S ^[1]; Bond, J R ^[2]

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1. NASA/Fermilab Astrophysics Center, P. O. Box 500 MS-209, Batavia, Illinois 60510 (US)
2. Canadian Institute for Advanced Research Program, Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto (Canada)

We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is {ital T}=ln({ital Ha}), where {ital H} and {ital a} are the local values of the Hubble parameter and the scale factor, since {ital T} is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background.

• OSTI ID: 5716832
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
645400 -- High Energy Physics-- Field Theory
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
FUNCTIONS
GRAVITATIONAL FIELDS
GREEN FUNCTION
HAMILTON-JACOBI EQUATIONS
HUBBLE EFFECT
LANGEVIN EQUATION
LATTICE FIELD THEORY
METRICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM FIELD THEORY
SCALAR FIELDS
STOCHASTIC PROCESSES