Equations of State in the Brans-Dicke cosmology

TL;DR

This paper explores the Brans-Dicke cosmological model with a potential, analyzing its ability to explain the universe's acceleration and its relation to $f(R)$ gravity, focusing on the phantom divide crossing.

Contribution

It introduces a power-law potential and dark matter interaction in Brans-Dicke theory, demonstrating the phantom divide crossing and connecting it to $f(R)$ gravity models.

Findings

Phantom divide crossing confirmed by native and effective equations of state.

Describes $f(R)$ gravity as a special case with similar phantom crossing behavior.

Provides a framework linking Brans-Dicke theory and $f(R)$ gravity for cosmological acceleration.

Abstract

We investigate the Brans-Dicke (BD) theory with the potential as cosmological model to explain the present accelerating universe. In this work, we consider the BD field as a perfect fluid with the energy density and pressure in the Jordan frame. Introducing the power-law potential and the interaction with the cold dark matter, we obtain the phantom divide which is confirmed by the native and effective equation of state. Also we can describe the metric $f(R)$ gravity with an appropriate potential, which shows a future crossing of phantom divide in viable $f(R)$ gravity models when employing the native and effective equations of state.