Bianchi type I Universe and instability of new agegraphic dark energy in Brans-Dicke theories

In this paper, we consider the new agegraphic dark energy (NADE) in a Bianchi type-I metric (which is a spatially homogeneous and anisotropic) in the framework of Brans-Dicke theory. For this purpose, we use the squared sound speed v(s)(2) whose sign determines the stability of the model. We explore the stability of this model in the presence/absence of interaction between dark energy and dark matter in both flat and non-isotropic geometry. The equation of state and the deceleration parameter of the new agegraphic dark energy in a anisotropic Universe is obtained. We show that the combination of Brans-Dicke field and new agegraphic dark energy can accommodate omega(Lambda) = -1 crossing for the equation of state of noninteracting dark energy. When an interaction between dark energy and dark matter is taken into account, the transition of omega(Lambda) to phantom regime can be more easily accounted when the Einstein field equations is being resort. In conclusion, we find evidences that the new agegraphic dark energy in BD theory can not lead to a stable Universe favored by observations at the present time. The anisotropy of the Universe decreases and the Universe transits to an isotropic flat FRW Universe accommodating the present acceleration.