Optimising Boltzmann codes for the Planck era

TL;DR

This paper evaluates and optimizes the numerical accuracy of the CAMB Boltzmann code for CMB predictions, demonstrating that with proper settings, numerical errors are minimized, ensuring reliable cosmological parameter estimation from future high-precision data.

Contribution

The study identifies key parameters affecting CAMB's accuracy and develops an optimization method to balance precision and computational efficiency.

Findings

Default settings can bias parameter estimates by several tenths of a standard deviation.

Optimized parameters significantly reduce numerical errors in the code.

Numerical errors are now a minor source of uncertainty compared to astrophysical factors.

Abstract

High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the Planck satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical error in the output of the Boltzmann codes used to calculate angular power spectra. In this work, we carry out an extensive study of the numerical accuracy of the public Boltzmann code CAMB, and identify a set of parameters which determine the error of its output. We show that at the current default settings, the cosmological parameters extracted from data of future experiments like Planck can be biased by several tenths of a standard deviation for the six parameters of the standard Lambda-CDM model, and potentially more seriously for extended models. We perform an optimisation procedure that leads the code to achieve sufficient precision while at the same time keeping the computation time within reasonable limits. Our conclusion is that the contribution of numerical errors to the theoretical uncertainty of model predictions is well under control -- the main challenges for more accurate calculations of CMB spectra will be of an astrophysical nature instead.