Crossing Phantom Boundary in $f(R)$ Modified Gravity : Jordan Frame vs Einstein Frame

TL;DR

This paper examines the ability of $f(R)$ gravity models to cross the phantom boundary in both Jordan and Einstein frames, revealing differences in their physical interpretations through the evolution of the equation of state parameter.

Contribution

It provides a comparative analysis of $f(R)$ gravity models in Jordan and Einstein frames, highlighting their distinct physical implications in cosmology.

Findings

The two conformal frames exhibit different physical behaviors.

Crossing the phantom boundary is possible in both frames but with different implications.

The evolution of the equation of state parameter serves as a tool to distinguish the frames.

Abstract

We study capability of $f(R)$ gravity models to allow crossing the phantom boundary in both Jordan and Einstein conformal frames. In Einstein frame, these models are equivalent to Einstein gravity together with a scalar field minimally coupled to gravity. This scalar degree of freedom appears as a quintessence field with a coupling with the matter sector. We investigate evolution of the equation of sate parameter for some cosmologically viable $f(R)$ gravity models in both conformal frames. This investigation (beyond mere theoretical arguments) acts as an operational tool to distinguish physical status of the two conformal frames. It shows that the two conformal frames have not the same physical status.