Equation of State for Dark Energy in Modified Gravity Theories

We explore the equation of state (EoS) for dark energy $w_{\mathrm{D}\mathrm{E}}$ in modified gravitational theories to explain the current accelerated expansion of the universe. We explicitly demonstrate that the future crossings of the phantom divide line of $w_{\mathrm{D}\mathrm{E}}=-1$ are the generic feature in the existing viable $f(R)$ gravity models. Furthermore, we show that the crossing of the phantom divide can be realized in the combined $f(T)$ theory constructed with the exponential and logarithmic terms. In addition, we investigate the effective EoS for the universe when the finite-time future singularities occur in non-local gravity.