Failures of Halofit model for computation of Fisher Matrices

We use a simple cosmological model with two parameters $(A_s, n_s)$ to illustrate the impact of using Halofit on error forecast based on Fisher information matrix for a $h^{-3} Gpc^3$ volume survey. We show that Halofit fails to reproduce well the derivatives of the power spectrum with respect to the cosmological parameters despite the good fit produced for its amplitude. We argue that the poor performance on the derivatives prediction is a general feature of this model and we exhibit the response function for the Halofit to show how it compares with the same quantity measured on simulations. The analytic structure of the Halofit response function points towards the origin of its weak performance at reproducing the derivatives of the non-linear power spectrum, which translates into unreliable Fisher information matrices.