Figures of Merit for Testing Standard Models: Application to Dark Energy Experiments in Cosmology

Given a standard model to test, an experiment can be designed to: (i) measure the standard model parameters; (ii) extend the standard model; or (iii) look for evidence of deviations from the standard model. To measure (or extend) the standard model, the Fisher matrix is widely used in cosmology to predict expected parameter errors for future surveys under Gaussian assumptions. In this article, we present a frame- work that can be used to design experiments such that it maximises the chance of finding a deviation from the standard model. Using a simple illustrative example, discussed in the appendix, we show that the optimal experimental configuration can depend dramatically on the optimisation approach chosen. We also show some simple cosmology calculations, where we study Baryonic Acoustic Oscillation and Supernove surveys. In doing so, we also show how external data, such as the positions of the CMB peaks measured by WMAP, and theory priors can be included in the analysis. In the cosmological cases that we have studied (DETF Stage III), we find that the three optimisation approaches yield similar results, which is reassuring and indicates that the choice of optimal experiment is fairly robust at this level. However, this may not be the case as we move to more ambitious future surveys.