Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame

TL;DR

This paper investigates the relationship between Jordan and Einstein frames in scalar-tensor cosmology, showing that the correspondence breaks down at the general relativity limit due to non-differentiability, affecting the interpretation of GR as an attractor.

Contribution

It demonstrates that the equivalence between Jordan and Einstein frames fails at the GR limit, highlighting the importance of frame choice in scalar-tensor cosmological models.

Findings

The scalar field phase portraits differ near the GR limit in the two frames.

The correspondence between frames is lost at the GR limit due to non-differentiability.

The attractor nature of GR depends on the frame chosen.

Abstract

We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence between the two frames is lost at this limit. To clarify the situation we analyse the dynamics of the scalar field in different frames for two distinct scalar-tensor cosmologies with specific coupling functions and demonstrate that the corresponding scalar field phase portraits are not equivalent for regions containing the general relativity limit. Therefore the answer to the question whether general relativity is an attractor for the theory depends on the choice of the frame.