Instability of QCD ghost dark energy model

We investigate the instability of the ghost dark energy model against perturbations in different cases. To this goal we use the squared sound speed $v_s^2$ whose sign determines the stability of the model. When $v_s^2<0$ the model is unstable against perturbation. At first we discuss the noninteracting ghost dark energy model in a flat FRW universe and find out that such a model is unstable due to the negativity of the $v_s^2$ in all epoches. The interacting ghost dark energy model in both flat and non-flat universe are studied in the next parts and in both cases we find that the squared sound speed of ghost dark energy is always negative. This implies that the perfect fluid for ghost dark energy is classically unstable against perturbations. In both flat and non flat cases we find that the instability of the model increases with increasing the value of the interacting coupling parameter.