Classification of dark energy models in the (w₀,w_a) plane

We classify dark energy models in a plane of observables that correspond to the common parameterization of a non-constant equation of state, w(a)=w_0 + w_a(1-a), where $a$ is the scale factor of the universe. The models fall into four classes and only two of these classes have a region of overlap in the observable plane. We perform a joint analysis of all Type Ia supernova (SNIa) data compiled by the High-Z SN Search Team (HZT) and the Supernova Legacy Survey (SNLS) and find that no class of models is excluded by current SNIa data. However, an analysis of large scale structure, Ly$\alpha$ forest and bias constraints from SDSS, the Gold SNIa data and WMAP data indicates that non-phantom barotropic models with a a positive sound speed are excluded at the 95% C.L.