Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity

TL;DR

This paper explores the relationship between phantom scalar dark energy models and modified F(R) gravity, revealing their mathematical equivalence, limitations, and differences in physical interpretation, especially near the Big Rip singularity.

Contribution

It demonstrates the conditions under which phantom scalar models can be mapped to modified F(R) gravity and highlights the physical differences arising from conformal factors.

Findings

Modified F(R) gravity is generally complex for phantom models.

Equivalence between the theories breaks down near the Big Rip.

Physical metrics differ due to time-dependent conformal factors.

Abstract

It is shown that phantom scalar models can be mapped into a mathematically equivalent, modified $F(R)$ gravity, which turns out to be complex, in general. Only for even scalar potentials is the ensuing modified gravity real. It is also demonstrated that, even in this case, modified gravity becomes complex at the region where the original phantom dark energy theory develops a Big Rip singularity. A number of explicit examples are presented which show that these two theories are not completely equivalent, from the physical viewpoint. This basically owes to the fact that the physical metric in both theories differ in a time-dependent conformal factor. As a result, an FRW accelerating solution, or FRW instanton, in the scalar-tensor theory may look as a deccelerating FRW solution, or a non-instantonic one, in the corresponding modified gravity theory.