Can luminosity distance measurements probe the equation of state of dark energy

Distance measurements to Type Ia supernovae (SNe Ia) at cosmological distances indicate that the Universe is accelerating and that a large fraction of the critical energy density exists in a component with negative pressure. Various hypotheses on the nature of this ``dark energy'' can be tested via their prediction for the equation of state of this component. If the dark energy is due to a scalar field, its equation of state will in general vary with time and is related to the potential of the field. We review the intrinsic degeneracies of luminosity distance measurements and compute the expected accuracies that can be obtained for the equation of state parameter from a realistic high statistic SNe Ia experiment.