Laura Wolz, Martin Kilbinger, Jochen Weller, Tommaso Giannantonio
We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters $w_0$ and $w_a$. For forecasts with fixed $w_a=0$, there is no qualitative discrepancy between the Fisher matrix approximation and the full likelihood via MCMC exploration, although there are significant quantitative differences; when marginalising over $w_a$ however, we find considerable disagreement between the two methods, since for geometrical probes the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function. More quantitatively, the Fisher method overestimates the DETF figure of merit (FoM) for purely geometrical probes by a factor of up to seven. Even in the cases including additional information from structure formation, such as weak lensing, where the likelihood is fairly elliptical, the posterior probability contours from the Fisher matrix estimation are too small: the resulting FoM is biased low by a factor of two. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that, especially for the purely geometrical probes, but also for tests of structure formation, the Fisher matrix is not the appropriate tool to produce reliable forecasts.
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http://arxiv.org/abs/1205.3984
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