Cosmological evolution of non-interacting and interacting holographic dark energy model in Brans-Dicke theory

The purpose of this paper is to study the dynamics of non-interacting and interacting holographic dark energy (HDE) models in the framework of Brans-Dicke (BD) cosmology. As system's infrared cutoff, we consider the future event horizon. The scalar function of BD theory is assumed to be a logarithmic form of scale factor, which is claimed to avoid a constant result for deceleration parameter. We investigate the cosmological implications of this model in detail. We obtain 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.