# 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}

}