# Holographic Dark Energy Model in Brans-Dicke Theory with Future Event Horizon

## TL;DR

This paper explores holographic dark energy within Brans-Dicke theory using a logarithmic scalar field form, analyzing cosmic evolution, phase transitions, and coincidence problems in both interacting and non-interacting models.

## Contribution

It introduces a novel logarithmic scalar field form in Brans-Dicke theory to study dark energy dynamics and cosmic acceleration.

## Key findings

- Model explains early inflation and late acceleration.
- Equation of state can cross the phantom divide.
- Logarithmic scalar field reduces coincidence problem.

## Abstract

In this paper, we study the dynamics of non-interacting and interacting holographic dark energy models in the framework of Brans-Dicke theory. As system's infra-red cut-off we consider the future event horizon. The motivation of this work is to use the logarithmic form of the Brans-Dicke scalar field, $\phi \propto ln(\alpha+\beta a)$, where $\alpha$ and $\beta$ are constants and `a' is the scalar factor as proposed Kumar and Singh in a recent work to study the new agegraphic dark energy models. We find the time-dependent equation of state parameter and deceleration parameter which describe the phase transition of the universe. We observe that the model explains the early time inflation and late time acceleration including matter-dominated phase. It is also observed that the equation of state parameter may cross phantom divide line in late time evolution. The cosmic coincidence problem is also discussed for both the models. We observe that this logarithmic form of Brans-Dicke scalar field is more appropriate to achieve a less acute coincidence problem in non-interacting model whereas a soft coincidence can be achieved if coupling parameter in interacting model has small value.