Generic feature of future crossing of phantom divide in viable $f(R)$ gravity models

TL;DR

This paper demonstrates that crossing the phantom divide line is a common feature in viable $f(R)$ gravity models and explores the oscillatory behavior of horizon entropy and Hubble parameter in future cosmological evolution.

Contribution

It shows that future crossing of the phantom divide line is a generic feature in viable $f(R)$ gravity models and analyzes the oscillatory behavior of horizon entropy.

Findings

Future crossing of the phantom divide line is generic in viable $f(R)$ models.

Cosmological horizon entropy oscillates over time.

The sign of the derivative of the Hubble parameter changes from negative to positive.

Abstract

We study the equation of state for dark energy and explicitly demonstrate that the future crossings of the phantom divide line $w_{\mathrm{DE}}=-1$ are the generic feature in the existing viable $f(R)$ gravity models. We also explore the future evolution of the cosmological horizon entropy and illustrate that the cosmological horizon entropy oscillates with time due to the oscillatory behavior of the Hubble parameter. The important cosmological consequence is that in the future, the sign of the time derivative of the Hubble parameter changes from negative to positive in these viable $f(R)$ gravity models.