Quantum mechanics of the scalar field in the new inflationary universe

Details Quantum mechanics of the scalar field in the new inflationary universe Quantum mechanics of the scalar field in the new inflationary universe

Oct 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..32.1899g&link_type=abstract

Physical Review D (Particles and Fields), Volume 32, Issue 8, 15 October 1985, pp.1899-1920

Mathematics

Probability

286

Particle-Theory And Field-Theory Models Of The Early Universe, Spontaneous Breaking Of Gauge Symmetries, Spontaneous And Radiative Symmetry Breaking

Scientific paper

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 Sit- ter 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.

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