Future Oscillations around Phantom Divide in f(R) Gravity

TL;DR

This paper investigates the potential for infinite future oscillations of dark energy's equation of state in f(R) gravity models, providing analytical conditions and numerical analysis of these phenomena.

Contribution

It proves that the number of phantom divide crossings in f(R) gravity can be infinite and derives conditions for their occurrence.

Findings

Number of crossings can be infinite.

Amplitude of oscillations decreases rapidly with scalaron mass.

Oscillations become negligible and occur in the distant future.

Abstract

It is known that scalar-tensor theory of gravity admits regular crossing of the phantom divide line $w_{\DE}=-1$ for dark energy, and existing viable models of present dark energy for its particular case -- $f(R)$ gravity -- possess one such crossing in the recent past, after the end of the matter dominated stage. It was recently noted that during the future evolution of these models the dark energy equation of state $w_{\DE}$ may oscillate with an arbitrary number of phantom divide crossings. In this paper we prove that the number of crossings can be infinite, present an analytical condition for the existence of this effect and investigate it numerically. With the increase of the present mass of the scalaron (a scalar particle appearing in $f(R)$ gravity) beyond the boundary of the appearance of such oscillations, their amplitude is shown to decrease very fast. As a result, the effect quickly becomes small and its beginning is shifted to the remote future.