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 $V\left(\phi \right)$ 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 $V\left(\phi \right)$ and $w_{\phi }$. Our results favor $w_{\phi }\simeq -1\mathrm{}$ at the present epoch, steadily increasing with redshift. A cosmological constant is consistent with our results.