Null Energy Condition and Dark Energy Models

Null Energy Condition (NEC) requires the equation of state (EoS) of the universe $w_u$ satisfy $w_u\ge -1$, which implies, for instance in a universe with matter and dark energy dominating $w_u=w_m{\mathrm{\Omega }}_m+w_{de}{\mathrm{\Omega }}_{de}=w_{de}{\mathrm{\Omega }}_{de}\ge -1$. In this paper we study constraints on the dark energy models from the requirement of the NEC. We will show that with ${\mathrm{\Omega }}_{de}\sim 0.7$, $w_{de}<-1$ at present epoch is possible. However, NEC excludes the possibility of $w_{de}<-1$ forever as happened in the Phantom model, but if $w_{de}<-1$ stays for a short period of time as predicted in the Quintom theory NEC can be satisfied. We take three examples of Quintom models of dark energy, namely the phenomenological EoS, the two-scalar-field model and the single scalar model with a modified Dirac-Born-Infeld (DBI) lagrangian to show how this happens.