Comparison of Frames: Jordan vs Einstein Frame for a Non-minimal Dark Energy Model

TL;DR

This paper compares the cosmological implications of a non-minimally coupled scalar field as dark energy in Jordan and Einstein frames, highlighting differences in phantom divide line crossing and solution stability.

Contribution

It demonstrates that non-minimal coupling allows phantom crossing in the Jordan frame but not in the Einstein frame after conformal transformation.

Findings

Jordan frame scalar field can cross the phantom divide line.

Conformal transformation to Einstein frame removes the crossing capability.

Stability and bouncing solutions differ between frames.

Abstract

We construct a dark energy model where a scalar field non-minimally coupled to gravity plays the role of the dark component. We compare cosmological consequences of this non-minimal coupling of the scalar field and gravity in the spirit of the dark energy paradigm in Jordan and Einstein frames. Some important issues such as phantom divide line crossing, existence of the bouncing solutions and the stability of the solutions are compared in these two frames. We show that while a non-minimally coupled scalar field in the Jordan frame is a suitable dark energy component with capability to realize phantom divide line crossing, its conformal transformation in the Einstein frame has not this capability. The conformal transformation from Jordan frame to Einstein frame transforms the equation of state parameter of the dark energy component to its minimal form with a redefined scalar field and in this case it is impossible to realize a phantom phase with possible crossing of the phantom divide line.