Pre-Inflation in the Presence of Conformal Coupling

TL;DR

This paper explores a conformally coupled massless scalar field in a closed universe's pre-inflation era, presenting exact solutions that connect smoothly to inflationary models, with implications for early universe cosmology.

Contribution

It introduces exact solutions for a conformally coupled scalar field in pre-inflation, linking pre-Big-Bang models to inflation with smooth matching conditions.

Findings

Exact solutions exist for conformal parameter <1/6.

Solutions can be smoothly matched to inflationary models.

The model accommodates Coleman-Weinberg potential at the onset of inflation.

Abstract

We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman-Weinberg one-loop potential, which is flat at the origin and drives the inflationary evolution. For positive values of the conformal parameter \xi, less than the critical value xi_c=(1/6), the model admits exact solutions with non-zero scale factor and zero initial Hubble parameter. Thus these solutions can be matched smoothly to the so called Pre-Big-Bang models. At the end of this pre-inflation era one can match inflationary solutions by specifying the form of the potential and the whole solution is of the class C^(1).