Quantum mechanics of the scalar field in the new inflationary universe

Journal Article · Tue Oct 15 00:00:00 EDT 1985 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.32.1899· OSTI ID:5014846

Guth, A H; Pi, S

An attempt is made to clarify the quantum theory of the ''slow-rollover'' phase transition which characterizes the new inflationary universe model. We discuss the theory of the upside-down harmonic oscillator as a toy model, with particular emphasis on the fact that the system can be described at late times by a classical probability distribution. An approximate but exactly soluble model for the scalar field is then constructed, based on three principal assumptions: (1) exact de Sitter expansion for all time; (2) a quadratic potential function which changes from stable to unstable as a function of time; and (3) an initial state which is thermal in the asymptotic past. It is proposed that this model would be the proper starting point for a perturbative calculation in more realistic models. The scalar field can also be described at late times by a classical probability distribution, and numerical calculations are carried out to illustrate how this distribution depends on the parameters of the model. For a suitable choice of these parameters, a sufficient period of inflation can be easily obtained. Density fluctuations can be calculated exactly in this model, and the results agree very well with those previously obtained using approximate methods.

• Research Organization: Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138
• DOE Contract Number: AC02-76ER03069
• OSTI ID: 5014846
• Journal Information: Phys. Rev. D; (United States), Vol. 32:8
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SCALAR FIELDS
QUANTUM MECHANICS
UNIVERSE
COUPLING CONSTANTS
HARMONIC OSCILLATOR MODELS
METRICS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
PROBABILITY
VACUUM STATES
MATHEMATICAL MODELS
MECHANICS
640106* - Astrophysics & Cosmology- Cosmology
645400 - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics