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 paper, we present a framework that can be used to design experiments that will maximize the chance of finding a deviation from the standard model. Using a simple illustrative example, discussed in Appendix A, we show that the optimal experimental configuration can depend dramatically on the optimization approach chosen. We also show some simple cosmology calculations, where we study baryonic acoustic oscillation and supernovae surveys. In doing so, we also show how external data, such as the positions of the cosmic microwave background peak measured by Wilkinson Microwave Anisotropy Probe, and theory priors can be included in the analysis. In the cosmological cases that we have studied (Dark Energy Task Force Stage III), we find that the three optimization 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.