  We study in this paper the perturbations of the quintom dark energy model and
the effects of quintom perturbations on the current observations. Quintom
describes a scenario of dark energy where the equation of state gets across the
cosmological constant boundary $w = -1$ during evolution. We present a new
method to show that the conventional dark energy models based on single
k-essence field and perfect fluid cannot act as quintom due to the
singularities and classical instabilities of perturbations around $w = -1$. One
needs to add extra degrees of freedom for successful quintom model buildings.
There are no singularities or classical instabilities in perturbations of
realistic quintom models and they are potentially distinguishable from the
cosmological constant. Basing on the realistic quintom models in this paper we
provide one way to include the perturbations for dark energy models with
parametrized equation of state across -1. Compare with those assuming no dark
energy perturbations, we find that the parameter space which allows the
equation of state to get across -1 will be enlarged in general when including
the perturbations.
