How to test stringy dark energy?

It is suggested, by using a covariant Lagrangian formalism to estimate the equation of state w=p/ρ, that stringy dark energy predicts w<-1, a negative pressure larger in magnitude than that for a cosmological constant or quintessence. This would lead to a later transition from decelerating to accelerating cosmological expansion; w=-4/3 is briefly considered as one illustrative example