Scalar Field Cosmologies With Inverted Potentials

TL;DR

This paper explores scalar field cosmologies with inverted potentials, demonstrating integrable models in general relativity that feature regular solutions evolving from a Big Bang to a de Sitter space.

Contribution

It provides a new analysis of scalar-tensor cosmologies in the Einstein frame, revealing integrable models with inverted double-well potentials unbounded from below.

Findings

Models have solutions regular in the future tending to de Sitter space.

Singularities in the Jordan frame correspond to Big Bang or Big Crunch in the Einstein frame.

Existence of fixed points in field dynamics at late times is clarified.

Abstract

Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.