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

Abstract

We investigate the issues of future oscillations around the phantom divide 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 provides the native equation of state $w_{\mathrm{DE}}$. On the other hand, the other has the different forms of energy density and pressure which do not obviously satisfy the continuity equation. This needs to introduce the effective equation of state $w_{\mathrm{eff}}$ to describe the $f(R)$-fluid, in addition to the native equation of state ${\tilde{w}}_{\mathrm{DE}}$. We confirm that future oscillations around the phantom divide occur in $f(R)$ gravities by introducing two types of equations of state. Finally, we point out that the singularity appears ar $x=x_c$ because the stability condition of $f(R)$ gravity violates.

23 pages, 10 figures, correcting typing mistake in title

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Cited by in corpus (4)

• Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era
• Some aspects of generalized modified gravity models
• Note on the equation of state of geometric dark-energy in f(R) gravity
• Late-time acceleration in the coupled Cubic Galileon models