Euclid: Validation of the MontePython forecasting tools

The mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. We expand and adjust the mock likelihoods of the software in order to match the exact recipes used in previous Fisher matrix forecasts for several probes: weak lensing cosmic shear, photometric galaxy clustering, the cross-correlation between the latter observables, and spectroscopic galaxy clustering. We also establish which precision settings are required when running the Einstein--Boltzmann solvers and in the context of Euclid. For the minimal cosmological model, extended to include dynamical dark energy, we perform Fisher matrix forecasts based directly on a numerical evaluation of second derivatives of the likelihood with respect to model parameters. We compare our results with those of previously validated Fisher codes using an independent method based on first derivatives of the observables. We show that such forecasts agree very well with previous Fisher forecasts published by the Euclid Collaboration, and also, with new forecasts produced by the code, now interfaced directly with the two Einstein--Boltzmann solvers and Moreover, to establish the validity of the Gaussian approximation, we show that the Fisher matrix marginal error contours coincide with the credible regions obtained when running Monte Carlo Markov Chains with while using the exact same mock likelihoods. The new forecast pipelines presented here are ready for use with additional cosmological parameters, in order to explore extended cosmological models.