Recent acceleration and future deceleration in Brans-Dicke theory

In this work, we have analysed the Barrow holographic dark energy model in the Brans-Dicke cosmology in the framework of the flat Friedmann-LemaitreRobertson-Walker universe. To discuss the cosmological implications of the model, we have considered a well motivated logarithmic form of Brans-Dicke scalar field. Barrow holographic dark energy is based on Barrow entropy rather than the standard Bekenstein-Hawking entropy. The component Delta with bounds 0 <= Delta <= 1 is the quantum-gravitational distortionwhich modifies holographic dark energy. The cosmological parameters like the equation of state parameter and the deceleration parameter are obtained to explain the evolution of the universe by using the various estimations of Barrow exponent Delta and other model parameters. We have observed that the equation of state parameter shows quintessence like behaviour at present and in future. The deceleration parameter shows recent phase transition of the universe (decelerated to accelerated expansion). Further, deceleration parameter shows decelerated expansion of the universe in future. We have discussed cosmic coincidence problem and found that it does not appear in the present model. The w(h) - w(h)' analysis of the model shows its similarity with some well known DE models in different time periods, however, over all evolution of the trajectories is quite different in comparison of well known DE models. Further, we show that our model satisfies the generalized second law of thermodynamics for suitable choice of model parameters.