Coupling of Brans-Dicke scalar field with Horava-Lifshitz gravity

We look for a Brans-Dicke type generalization of Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the low energy limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous, isotropic cosmology and study the effects of the new terms appearing in the model.