Future cosmological evolution in f (R) gravity using two equations of state parameters

We investigate the issues of future oscillations around the phantom divide (FOPD) for f (R) gravity. For this purpose, we introduce two types of energy density and pressure arisen from the f (R)-higher order curvature terms. One has the conventional energy density and pressure even in the beginning of the Jordan frame, whose continuity equation defines the native equation of state w(DE). On the other hand, the other has the different energy density and pressure which do not obviously satisfy the continuity equation. This needs to introduce the effective equation of state w(eff) to describe the f (R)-fluid, in addition to the native equation of state (w) over tilde (DE). We show that the FOPD occur in f (R) gravities by introducing two types of equation of state. Finally, we point out that the singularity appears ar x = x(c) because the stability condition of f (R) gravity violates.