Phantom Crossing and Oscillating Dark Energy with $F(R)$ Gravity

TL;DR

The paper investigates whether dynamical dark energy that crosses the phantom divide and even oscillates at late times can be realized within $F(R)$ gravity without invoking phantom fields. It develops theoretical conditions for inverse and apparent phantom crossing, and constructs oscillating-Hubble-rate scenarios, illustrating how $f(R)$-driven effects or curvature-dependent dark matter can engender such behavior. Two explicit, cosmologically viable $F(R)$ models are analyzed numerically using statefinder diagnostics, showing late-time crossing and strong oscillations in the dark-energy equation of state that remain compatible with Planck data and DESI hints. The work argues that $F(R)$ gravity offers a natural extension of GR capable of producing phantom-to-quintessence transitions and DE oscillations with no phantom degrees of freedom, highlighting its potential as a realistic framework for late-time cosmology.

Abstract

In this work, we shall consider how a dynamical oscillating and phantom crossing dark energy era can be realized in the context of $F(R)$ gravity. We approach the topic from a theoretical standpoint considering all the conditions that may lead to a consistent phantom crossing behavior and separately how the $F(R)$ gravity context may realize oscillating dark energy era. Apart from our qualitative considerations, we study in a quantitative way two $F(R)$ gravity dark energy models which are viable cosmologically and also exhibit simultaneously phantom crossing behavior and also oscillating dark energy. We consider these models by solving numerically the field equations using appropriate statefinder parameters engineered for dark energy studies. As we show, $F(R)$ provides a natural extension of Einstein's general relativity which can naturally realize a transition from a phantom era to a quintessential era, a feature supported by recent observational data, without resorting to phantom scalar fields to realize the phantom evolution.

Figures (2)

• Figure 1: Plots of the deceleration parameter $q(z)$ (upper left plot) and the DE EoS parameter $w_\mathrm{DE}(z)$ (right and bottom plot) as functions of the redshift for the model Eq. (\ref{['fr24']}) for $b=20\Lambda$, $c=2$, and $R_0={m_s}^2/0.00091$.
• Figure 2: Plots of the deceleration parameter $q(z)$ (upper left plot) and the DE EoS parameter $w_\mathrm{DE}(z)$ (right and bottom plot) as functions of the redshift for the model of Eq. (\ref{['frhu']}) with $\alpha=1.4 \Lambda$, $b=1$, $c=0.2$ , $d=0.04$, $R_0={m_s}^2$, and $n=0.3$.