Can dark energy evolve to the phantom?

Dark energy with the equation of state w(z) rapidly evolving from the dustlike (w≃0 at z∼1) to the phantomlike (-1.2≲w≲-1 at z≃0) 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(φ,∇_μφ) dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states (φ,φ˙) with w≥-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 ∇_μφ. The result is insensitive to topology of the Friedmann universe as well.