Crossing of Phantom Divide in $F(R)$ Gravity

TL;DR

This paper reconstructs an $F(R)$ gravity model that exhibits crossing of the phantom divide and discusses how to avoid Big Rip singularities by modifying the model.

Contribution

It provides an explicit $F(R)$ gravity model with phantom divide crossing and proposes methods to prevent Big Rip singularities.

Findings

The reconstructed $F(R)$ model allows crossing of the phantom divide.

Big Rip singularity can occur in the model.

Adding an $R^2$ term or non-singular $F(R)$ theories can avoid singularities.

Abstract

An explicit model of $F(R)$ gravity with realizing a crossing of the phantom divide is reconstructed. In particular, it is shown that the Big Rip singularity may appear in the reconstructed model of $F(R)$ gravity. Such a Big Rip singularity could be avoided by adding $R^2$ term or non-singular viable $F(R)$ theory to the model because phantom behavior becomes transient.