Can dark energy evolve to the phantom?

Dark energy with the equation of state w(z) rapidly evolving from the dustlike (wsimilar or equal to0 at zsimilar to1) to the phantomlike (-1.2less than or similar towless than or similar to-1 at zsimilar or equal to0) has been recently proposed as the best fit for the supernovae Ia data. Assuming that a dark energy component with an arbitrary scalar-field Lagrangian p(phi,del(mu)phi) dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states (phi,phi) with wgreater than or equal to-1 to those with w<-1 or vice versa. We have found that generally such transitions are physically implausible because they are either realized by a discrete set of trajectories in the phase space or are unstable with respect to the cosmological perturbations. This conclusion is confirmed by a comparison of the analytic results with numerical solutions obtained for simple models. Without the assumption of the dark energy domination, this result still holds for a certain class of dark energy Lagrangians, in particular, for Lagrangians quadratic in del(mu)phi. The result is insensitive to topology of the Friedmann universe as well.