Reconstructing the Cosmic Equation of State from Supernova Distances

Observations of high-redshift supernovae indicate that the Universe is accelerating. Here we present a model-independent method for estimating the form of the potential V(phi) of the scalar field driving this acceleration, and the associated equation of state w(phi). Our method is based on a versatile analytical form for the luminosity distance D(L), optimized to fit observed distances to distant supernovae and differentiated to yield V(straight phi) and w(straight phi). Our results favor w(phi) approximately -1 at the present epoch, steadily increasing with redshift. A cosmological constant is consistent with our results.