Inflationary Solutions in Quantum Cosmology

TL;DR

This paper demonstrates that inflationary phases are a common feature in certain quantum cosmology models, specifically in minisuperspace scenarios with a closed universe and scalar fields, addressing key early universe problems.

Contribution

It proves that inflation naturally arises in the Hartle-Hawking quantum cosmology framework for specific minisuperspace models with scalar fields.

Findings

Inflationary phase is a general property in the considered models.

Conditions for solving horizon and flatness problems are derived.

Evolution of the scale factor and scalar field is explicitly obtained.

Abstract

We prove that in the Hartle-Hawking approach to quantum cosmology the existence of an inflationary phase is a general property of minisuperspace models given by a closed Friedmann-Robertson-Walker universe containing a massless scalar field with a $\lambda\phi^{n}$ self-interaction. The evolution in time of the cosmic scale factor and of the scalar field in the very early universe is derived, together with the conditions to be satisfied in order to solve the horizon and flatness problems.