Describing variations of the Fisher-matrix across parameter space

Abstract

Forecasts in cosmology, both with Monte Carlo Markov-chain methods and with the Fisher-matrix formalism, depend on the choice of the fiducial model because both the signal strength of any observable and the model non-linearities linking observables to cosmological parameters vary in the general case. In this paper we propose a method for extrapolating Fisher-forecasts across the space of cosmological parameters by constructing a suitable basis. We demonstrate the validity of our method with constraints on a standard dark energy model extrapolated from a ΛCDM-model, as can be expected from two-bin weak lensing tomography with an Euclid-like survey, in the parameter pairs (Ωm, σ8), (ωm, w0) and (w0, wa). Our numerical results include very accurate extrapolations across a wide range of cosmological parameters in terms of shape, size and orientation of the parameter likelihood, and a decomposition of the change of the likelihood contours into modes, which are straightforward to interpret in a geometrical way. We find that in particular the variation of the dark energy figure of merit is well captured by our formalism.