Multiple kinetic k-essence, phantom barrier crossing and stability

We investigate models of dark energy with purely kinetic multiple k- essence sources that allow for the crossing of the phantom divide line, without violating the conditions of stability. It is known that with more than one kinetic k-field one can possibly construct dark energy models whose equation of state parameter w(x) crosses -1 (the phantom barrier) at recent red-shifts, as indicated by the Supernova Ia and other observational probes. However, such models may suffer from cosmological instabilities, as the effective speed of propagation c(x) of the dark energy density perturbations may become imaginary while the w(x) = -1 barrier is crossed. Working out the expression for c(x) we show that multiple kinetic k-essence fields do indeed lead to a w(x) = -1 crossing dark energy model, satisfying the stability criterion c(x)(2) >= 0 as well as the condition c(x) <= 1 (in natural units), which implies that the dark energy is not super-luminal. As a specific example, we construct a phantom barrier crossing model involving three k-fields for which c(x) is a constant, lying between 0 and 1. The model fits well with the latest Supernova Ia Union data, and the best fit shows that w(x) crosses -1 at red-shift z similar to 0.2, whereas the dark energy density nearly tracks the matter density at higher red-shifts.