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.