Failures of Halofit model for computation of Fisher Matrices: a response function analysis

The response function of a linear system undergoing a non-linear transformation measures the sensitivity of the non-linear output with respect to the initial linear state. This concept can also be applied to the non-linear growth of structures in the Universe. In this paper, we study the response function for the Halofit model, we present its analytic structure and we compare its theoretical prediction with the one as measured from simulations. We find a major departure between the two. We argue that a consequence of unmatched response functions is an intrinsic theoretical limitation on Halofit to predict the derivatives of the non-linear power spectrum with respect to cosmological parameters, and hence a possible systematic effect on Fisher matrices based forecasts using Halofit. In particular, we use a simple cosmological model with two parameters (A,, ris) to illustrate the impact of using Halofit for this kind of forecasts for a 1 h-3 Gpc3 volume survey. We report a maximum impact on the figure of merit of 20 per cent.