Role of the Brans-Dicke scalar in the holographic description of dark energy

We study cosmological application of the holographic energy density in the Brans-Dicke theory. Considering the holographic energy density as a dynamical cosmological constant, it is more natural to study it in the Brans-Dicke theory than in general relativity. Solving the Friedmann and Brans-Dicke field equations numerically, we clarify the role of Brans-Dicke field during evolution of the universe. When the Hubble horizon is taken as the IR cutoff, the equation of state (wΛ) for the holographic energy density is determined to be 53 when the Brans-Dicke parameter ω goes infinity. This means that the Brans-Dicke field plays a crucial role in determining the equation of state. For the particle horizon IR cutoff, the Brans-Dicke scalar mediates a transition from wΛ=−1/3 (past) to wΛ=1/3 (future). If a dust matter is present, it determines future equation of state. In the case of future event horizon cutoff, the role of the Brans-Dicke scalar and dust matter are turned out to be trivial, whereas the holographic energy density plays an important role as a dark energy candidate with wΛ=−1.