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.
