Distinguishing Among Scalar Field Models of Dark Energy

We show that various scalar field models of dark energy predict a degenerate luminosity distance history of the Universe and thus cannot be distinguished by supernovae measurements alone. In particular, models with a vanishing cosmological constant (the value of the potential at its minimum) are degenerate with models with a positive or negative cosmological constant whose magnitude can be as large as the critical density. Adding information from CMB anisotropy measurements does reduce the degeneracy somewhat but not significantly. Our results indicate that a theoretical prior on the preferred form of the potential and the field's initial conditions may allow one to quantitatively estimate model parameters from the data. Without such a theoretical prior only limited qualitative information on the form and parameters of the potential can be extracted, even from very accurate data.