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 as well as the model nonlinearities 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 ba- sis. 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 2-bin weak lensing to- mography with a Euclid-like survey, in the parameter pairs $(Ω_\text{m},σ_8)$, $(Ω_\text{m}, w_0)$ and $(w_0, w_\text{a})$. Our numerical results include very accurate extrapolations across a wide range of cosmo- logical 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.