General dynamics of quintessence fields: Comparison with type Ia SNe

This work discusses some preliminary results for observational constraints on quintessence fields using dynamical system tools consisting in finding the critical points in the phase space of the system as well as determine the special trajectories which connect physically relevant critical points. For cosmological dynamics, attractor trajectories exist in the form of the heteroclinic trajectories of the phase space. The approach is tested by observing the behavior of the quintessence fields, the monotonic freezing and the monotonic thawing. The values obtained for the roll parameter λ and the variables of the approach are the same in both cases which surprisingly corresponds to the cosmological constant behavior.