Sign-changeable interacting agegraphic dark energy in Brans-Dicke cosmology

We explore a spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) universe that is filled with agegraphic dark energy (ADE) with mutual interaction with pressureless dark matter in the background of Brans-Dicke (BD) theory. We consider both original and a new type of ADE (NADE) and further assume that the sign of the interaction term can change during the history of the universe. We obtain the equation of the state parameter, the deceleration parameter, and the evolutionary equation for the sign-changeable interacting ADE and NADE in BD cosmology. We find that in both models, the equation of the state parameter, w(D), cannot cross the phantom line, although they can predict the universe evolution from the early deceleration phase to the late time acceleration, compatible with observations. We also investigate the sound stability of these models and find out that both models cannot show a signal of stability for different model parameters.