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Title: Quantum mechanics of the scalar field in the new inflationary universe

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
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
OSTI Identifier:
5014846
DOE Contract Number:  
AC02-76ER03069
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys. Rev. D; (United States); Journal Volume: 32:8
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Guth, A.H., and Pi, S.. Quantum mechanics of the scalar field in the new inflationary universe. United States: N. p., 1985. Web. doi:10.1103/PhysRevD.32.1899.
Guth, A.H., & Pi, S.. Quantum mechanics of the scalar field in the new inflationary universe. United States. doi:10.1103/PhysRevD.32.1899.
Guth, A.H., and Pi, S.. Tue . "Quantum mechanics of the scalar field in the new inflationary universe". United States. doi:10.1103/PhysRevD.32.1899.
@article{osti_5014846,
title = {Quantum mechanics of the scalar field in the new inflationary universe},
author = {Guth, A.H. and Pi, S.},
abstractNote = {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.},
doi = {10.1103/PhysRevD.32.1899},
journal = {Phys. Rev. D; (United States)},
number = ,
volume = 32:8,
place = {United States},
year = {Tue Oct 15 00:00:00 EDT 1985},
month = {Tue Oct 15 00:00:00 EDT 1985}
}