Instability of scalar perturbation in a phantomic cosmological scenario

Scalar perturbations can grow during a phantomic cosmological phase as the big rip is approached, in spite of the high accelerated expansion regime, if the equation of state is such that $\frac{p}{\rho} = \alpha < - {5/3}$. It is shown that such result is independent of the spatial curvature. The perturbed equations are exactly solved for any value of the curvature parameter $k$ and of the equation of state parameter $\alpha$. Growing modes are found asymptotically under the condition $\alpha < - {5/3}$. Since the Hubble radius decreases in a phantom universe, such result indicates that a phantom scenario may not survive longtime due to gravitational instability.