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New Agegraphic Dark Energy in Brans-Dicke Theory

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory which is a natural extension of the Einstein's general relativity. In this framework the form of the new agegraphic dark energy density takes as $ρ_{q} =3n^2 Φ(t)η^{-2}$, where $η$ is the conformal age of the universe and $Φ(t)$ is the Brans-Dicke scalar field representing the inverse of the time-variable Newton's constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide $w=-1$ during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans-Dicke theory with that in the Einstein's theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans-Dicke theory.