Evaluating Dark Energy Probes using Multi-Dimensional Dark Energy Parameters

We investigate the value of future dark energy experiments by modeling their ability to constrain the dark energy equation of state. Similar work was recently reported by the Dark Energy Task Force (DETF) using a two dimensional parameterization of the equation of state evolution. We examine constraints in a nine dimensional dark-energy parameterization, and find that the best experiments constrain significantly more than two dimensions in our 9D space. Consequently the impact of these experiments is substantially beyond that revealed in the DETF analysis, and the estimated cost per ``impact'' drops by about a factor of ten as one moves to the very best experiments. The DETF conclusions about the relative value of different techniques and of the importance of combining techniques are unchanged by our analysis.