Interacting Holographic Dark Energy model in Brans-Dicke cosmology and coincidence problem

TL;DR

This paper explores an interacting holographic dark energy model within Brans-Dicke cosmology, analyzing its dynamics and fixed points to address the cosmic coincidence problem for different horizon cut-offs.

Contribution

It introduces a detailed dynamical analysis of the model with both future event horizon and Hubble horizon cut-offs, showing near resolution of the coincidence problem.

Findings

Fixed points and attractors identified in the model.

Cosmic coincidence problem is nearly resolved for various parameters.

Model dynamics depend on the choice of horizon cut-off.

Abstract

We study the dynamics of interacting holographic dark energy model in Brans-Dicke cosmology for the future event horizon and the Hubble horizon cut-offs. We determine the system of first-order differential equations for the future event horizon and Hubble horizon cut-offs, and obtain the corresponding fixed points, attractors, repellers and saddle points. Finally, we investigate the cosmic coincidence problem in this model for the future event horizon and Hubble horizon cut-offs and find that for both cut-offs and for a variety of Brans-Dicke parameters the coincidence problem is almost resolved.