The cosmological constant and quintessence

We study the possibility of parameterizing the cosmological constant as the contribution of a scalar field. Scalar field potential are not uniquely determined by symmetries so we analyze what kind of scalar potentials leads to an interpretation of the scalar energy density as quintessence, i.e. a slow varying cosmological constant. All model dependence is given in terms of $−V′/V$ and we study all possible asymptotic limits. Finally, we show that during the accelerating period the expansion of the universe is model independent.