Optimising Boltzmann codes for the PLANCK era

Abstract

High precision measurements of the Cosmic Microwave Background (CMB)anisotropies, as can be expected from the PLANCK satellite, willrequire high-accuracy theoretical predictions as well. One possiblesource of theoretical uncertainty is the numerical error in the outputof the Boltzmann codes used to calculate angular power spectra. Inthis work, we carry out an extensive study of the numerical accuracyof the public Boltzmann code CAMB, and identify a set ofparameters which determine the error of its output. We show that atthe current default settings, the cosmological parameters extractedfrom data of future experiments like Planck can be biased by severaltenths of a standard deviation for the six parameters of the standardΛCDM model, and potentially more seriously for extendedmodels. We perform an optimisation procedure that leads the code toachieve sufficient precision while at the same time keeping thecomputation time within reasonable limits. Our conclusion is that thecontribution of numerical errors to the theoretical uncertainty ofmodel predictions is well under control—the main challenges formore accurate calculations of CMB spectra will be of an astrophysicalnature instead.