Scaling solution for cosmological fluctuations and large-scale structure

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

DOI:https://doi.org/10.1103/PhysRevD.45.3441· OSTI ID:7114157

Yi, I; Vishniac, E T ^[1]

---

1. Astronomy Department, University of Texas, Austin, Texas 78712 (United States)

We discuss the nonlinear multiplicative stochastic behavior of chaotic inflation with an emphasis on the relevance of the scaling'' effect for large-scale structure formation. We derive a simple criterion for the appearance of scaling behavior in the {lambda}{phi}{sup 4} inflaton model in an asymptotic limit which remains valid throughout the inflationary epoch. We show explicitly that in this limit the onset of the scaling regime does not require any special initial conditions and that it is independent of the self-coupling constant {lambda}. A decrease in the dispersion of field fluctuations at late times is seen in the course of stochastic evolution, and shown to follow from the squeezing'' of probability distributions due to the nonlinear stochastic effect. Non-Gaussian statistics in adiabatic fluctuations are important only for superhorizon scales and the scaling regime does not lead to any significant statistical properties on currently observable scales. However, the scaling effect gives some cosmological consequences very different from what we expect in the naive diffusion approximation for quantum fluctuations. We show that the classical treatment (deterministic) of the inflaton field (essentially a quantum-mechanical object) becomes valid towards the end of inflation because of nonlinear effects.

• OSTI ID: 7114157
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 45:10; 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
COSMOLOGICAL MODELS
STOCHASTIC PROCESSES
COUPLING CONSTANTS
FOKKER-PLANCK EQUATION
HUBBLE EFFECT
NONLINEAR PROBLEMS
PROBABILITY
QUANTUM MECHANICS
SCALAR FIELDS
SCALING LAWS
UNIVERSE
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)