Perturbations of the Quintom Models of Dark Energy and the Effects on Observations

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.