Equation of State for Dark Energy in Modified Gravity Theories

TL;DR

This paper investigates the behavior of dark energy's equation of state in various modified gravity theories, highlighting the generic crossing of the phantom divide in $f(R)$ models and exploring singularities in non-local gravity.

Contribution

It demonstrates the universal crossing of the phantom divide in viable $f(R)$ models and constructs $f(T)$ models with such crossings, also analyzing singularities in non-local gravity.

Findings

Future crossing of $w_{DE}=-1$ is generic in $f(R)$ models.

Crossing of the phantom divide is achievable in combined $f(T)$ theories.

Finite-time future singularities are studied in non-local gravity.

Abstract

We explore the equation of state (EoS) for dark energy $w_{\mathrm{DE}}$ 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 $w_{\mathrm{DE}}=-1$ 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.