Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

TL;DR

This paper explores how transformations between Jordan and Einstein frames relate to crossing singularities in flat Friedmann universes, revealing that regular evolution in one frame can correspond to singularities in the other, and develops methods to extend cosmological models beyond these singularities.

Contribution

It provides a detailed analysis of frame transformations and their role in singularity crossing, introducing a method for continuing cosmological evolutions beyond singularities.

Findings

Regular evolution in one frame can correspond to crossing singularities in another

Developed a method for extending cosmological models beyond singularities

Compared approach with other recent methods for singularity crossing

Abstract

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.