Holographic dark energy in Brans-Dicke theory with logarithmic form of scalar field

TL;DR

This paper proposes a holographic dark energy model within Brans-Dicke theory using a logarithmic scalar field, explaining early inflation, deceleration, and late acceleration, and addressing the cosmic coincidence problem.

Contribution

It introduces a novel logarithmic form of the Brans-Dicke scalar field to improve holographic dark energy models and demonstrates its effectiveness in explaining cosmic acceleration phases.

Findings

The model shows early inflation and late acceleration phases.

The equation of state parameter can cross the phantom divide.

The model addresses the cosmic coincidence problem with a constant density ratio.

Abstract

In this paper, an interacting holographic dark energy model with Hubble horizon as an infra-red cut-off is considered in the framework of Brans-Dicke theory. We propose a logarithmic form $\phi \propto ln(\alpha+\beta a)$ of the Brans-Dicke scalar field to alleviate the problems of interacting holographic dark energy models in Brans-Dicke theory. We find that the equation of state parameter $w_h$ and deceleration parameter $q$ are negative in the early time which shows the early time inflation. During the evolution the sign of parameter $q$ changes from negative to positive which means that the Universe expands with decelerated rate whereas the sign of $w_h$ may change or remain negative throughout the evolution depending on the values of parameters. It is also observed that $w_h$ may cross the phantom divide line in the late time evolution. The sign of $q$ changes from positive to negative during late time of evolution which explains the late time accelerated expansion of the Universe. Thus, we present a unified model of holographic dark energy which explains the early time acceleration (inflation), medieval time deceleration and late time acceleration. We also discuss the cosmic coincidence problem. We obtain a time-varying density ratio of holographic dark energy to dark matter which is a constant of order one ($r\sim \mathcal{O}(1)$) during early and late time evolution. Therefore, our model successfully resolves the cosmic coincidence problem.