Measure of the impact of future dark energy experiments based on discriminating power among quintessence models

We evaluate the ability of future data sets to discriminate among different quintessence dark energy models. This approach gives an alternative (and complementary) measure for assessing the impact of future experiments, as compared with the large body of literature that compares experiments in abstract parameter spaces (such as the well-known w(0) - w(a) parameters) and more recent work that evaluates the constraining power of experiments on individual parameter spaces of specific quintessence models. We use the Dark Energy Task Force (DETF) models of future data sets and compare the discriminative power of experiments designated by the DETF as stages 2, 3, and 4 (denoting increasing capabilities). Our work reveals a minimal increase in discriminating power when comparing stage 3 to stage 2, but a very striking increase in discriminating power when going to stage 4 (including the possibility of completely eliminating some quintessence models). We also see evidence that even modest improvements over C DETF stage 4 (which many believe are realistic) could result in even more dramatic discriminating power among quintessence dark energy models. We develop and demonstrate the technique of using the independently measured modes of the equation of state (derived from principle component analysis) as a common parameter space in which to compare the different quintessence models, and we argue that this technique is a powerful one. We use the PNGB, Exponential, Albrecht-Skordis, and Inverse Tracker (or inverse power law) quintessence models for this work. One of our main results is that the goal of discriminating among these models sets a concrete measure on the capabilities of future dark energy experiments. Experiments have to be somewhat better than DETF stage 4 simulated experiments to fully meet this goal.