Probing cosmological parameters with the CMB: Forecasts from full Monte   Carlo simulations
  The Fisher matrix formalism has in recent times become the standard method for predicting the precision with which various cosmological parameters can be extracted from future data. This approach is fast, and generally returns accurate estimates for the parameter errors when the individual parameter likelihoods approximate a Gaussian distribution. However, where Gaussianity is not respected (due, for instance, to strong parameter degeneracies), the Fisher matrix formalism loses its reliability. In this paper, we compare the results of the Fisher matrix approach with those from Monte Carlo simulations. The latter method is based on the publicly available CosmoMC code, but uses synthetic realisations of data sets anticipated for future experiments. We focus on prospective cosmic microwave background (CMB) data from the Planck satellite, with or without CMB lensing information, and its implications for a minimal cosmological scenario with eight parameters and an extended model with eleven parameters. We show that in many cases, the projected sensitivities from the Fisher matrix and the Monte Carlo methods differ significantly, particularly in models with many parameters. Sensitivities to the neutrino mass and the dark matter fraction are especially susceptible to change. 
Laurence Perotto, Julien Lesgourgues, Steen Hannestad, Huitzu Tu,   Yvonne Y.Y. Wong