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We study the stability of the ghost dark energy model versus perturbation.Since this kind of dark energy is instable in Einsteinian general relativitytheory, then we study a new type of Brans-Dicke theory which has non-minimalcoupling with matter which is called chameleon Brans-Dicke (CBD) model ofgravity. Due to this coupling the equation of conservation energy is modified.For considering the stability of the model we use the adiabatic squared soundspeed, $c_s^2$, whose sign of it determines the stability of the model in whichfor $c_s^2 >0 $ the model is stable and for $c_s^2 <0 $ the model is instable.However, we study the interacting and non-interacting version of chameleonBrans-Dicke ghost dark energy (CBDGDE) with cold dark matter in non flat FLRWmetric. We show that in all cases of investigation the model is stable with asuitable choice of parameters.

Stability of Ghost Dark Energy in CBD Model of Gravity