Reconstructing the Cosmic Equation of State from Supernova distances

Observations of high-redshift supernovae indicate that the universe is accelerating. Here we present a {\em model-independent} method for estimating the form of the potential $V(\varphi )$ of the scalar field driving this acceleration, and the associated equation of state $w_{\varphi }$. 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 $V(\varphi )$ and $w_{\varphi }$. Our results favor $w_{\varphi }\simeq -1$ at the present epoch, steadily increasing with redshift. A cosmological constant is consistent with our results.