f(R) Gravitation: Equivalence of Frames Upon a Conformal Transformation

TL;DR

This paper examines the mathematical and physical relationship between Jordan and Einstein frames in f(R) gravity, highlighting how conformal transformations can influence singularities and the potential implications for gravitational theory.

Contribution

It demonstrates that singularities in the Ricci scalar can differ between frames and proposes that conformal field dynamics may prevent singularity formation in the Jordan frame.

Findings

Ricci scalar can be singular in JF but finite in EF

Absence of singularity in EF allows large Ricci curvature values

Conformal field dynamics may prevent singularities in JF

Abstract

We investigate the behavior of the Ricci scalar in the Jordan (JF) and Einstein (EF) frames, in the context of f(R) gravitation. We discuss the physical equivalence of these two representations of the theory, which are mathematically equivalent and whose metrics are connected by a conformal transformation. We find that it is possible for this quantity to be singular in the JF but finite in the EF, if the conformal transformation that connects the frames is singular at the same point as the JF Ricci scalar. The absence of this physical singularity in the EF could be used as an argument against the physical equivalence of the frames. A plot of the EF potential as a function of the associated conformal field shows that the absence of the singularity allows the field to assume values associated to arbitrarily large values of the Ricci curvature. A conjecture is then proposed: the dynamics of the conformal field can be interpreted as a mechanism that can prevent the creation of singularities in the JF.