Crossing of the phantom divide in modified gravity

TL;DR

This paper constructs a modified gravity model allowing crossing of the phantom divide, analyzes its singularities in different frames, and explores the stability of solutions under quantum corrections.

Contribution

It presents an explicit model of modified gravity with phantom divide crossing and examines the relation between scalar field theories and $F(R)$ gravity via conformal transformations.

Findings

Big Rip singularity in Jordan frame

Singularity becomes infinite-time in Einstein frame

Stable solutions under quantum conformal anomaly

Abstract

We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (i.e., in the so-called Jordan frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (i.e., in the so-called Einstein frame) the singularity becomes the infinite-time one. Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitational theories by using the inverse conformal transformation. It is demonstrated that the scalar field theories describing the non-phantom phase (phantom one with the Big Rip) can be represented as the theories of real (complex) $F(R)$ gravity through the inverse (complex) conformal transformation. We also study a viable model of modified gravity in which the transition from the de Sitter universe to the phantom phase can occur. In addition, we explore the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction coming from conformal anomaly.