Motivated by the recent works of one of us (Karami and Fehri, Int. J. Theor. Phys. 49:1118, 2010; Phys. Lett. B 684:61, 2010), we study the holographic dark energy in BransDicke gravity with the Granda-Oliveros cut-off proposed recently in literature. We find out that when the present model is combined with Brans-Dicke field the transition from normal state where w D > −1 to the phantom regime where w D < −1 for the equation of state of dark energy can be more easily achieved for than when resort to the Einstein field equations is made. Furthermore, the phantom crossing is more easily achieved when the matter and the holographic dark energy undergo an exotic interaction. We also calculate some relevant cosmological parameters and their evolution.

In the derivation of holographic dark energy density, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity, string theory and black hole physics. In this paper, we study cosmological implication of the interacting entropy-corrected holographic dark energy model in the framework of Brans-Dicke cosmology. We obtain the equation of state and the deceleration parameters of the entropy-corrected holographic dark energy in a non-flat Universe. As system's IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L = ar(t). We find out that when the entropy-corrected holographic dark energy is combined with the Brans-Dicke field, the transition from normal state where w D > −1 to the phantom regime where w D < −1 for the equation of state of interacting dark energy can be more easily achieved for than when resort to the Einstein field equations is made.

Considering the power-law corrections to the black hole entropy, which appear in dealing with the entanglement of quantum fields inside and outside the horizon, the holographic energy density is modified accordingly. In this paper we study the power-law entropy-corrected holographic dark energy in the framework of Brans-Dicke theory. We investigate the cosmological implications of this model in detail. We also perform the study for the new agegraphic dark energy model and calculate some relevant cosmological parameters and their evolution. As a result we find that this model can provide the present cosmic acceleration and even the equation of state parameter of this model can cross the phantom line w D = −1 provided the model parameters are chosen suitably.

In this research, the strong coupling constants of the s0 K vertices are evaluated, using the three-point QCD sum rules. In order to calculate the coupling constant of each vertex, either the kaon or the charmed meson is considered as the off-shell particle.The basic g parameter, in the heavy quark effective theory, is related to the coupling constants of D * D * s K and D * D s K. Our obtained value for g parameter is 0.24 ± 0.09, which is in good agreement with the lower limits of the other existing predictions.

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