The Cosmic Linear Anisotropy Solving System (CLASS) III: Comparision with CAMB for LambdaCDM

TL;DR

This work cross-validates two independent Boltzmann codes, CLASS and CAMB, for minimal LambdaCDM with a shared recombination history and line-of-sight integration, demonstrating agreement to about 0.01% for CMB spectra and the matter power spectrum. It identifies key numerical sources of residual differences—primarily thermodynamics sampling and Bessel-function treatments—and develops reference precision settings (e.g., CLASS:01, CLASS:02) and Planck-like likelihood-based degradation to control Delta chi^2. The authors show that, at fixed target accuracy, CLASS runs ~2.5× faster than CAMB on a single processor, underscoring substantial gains in computational efficiency for parameter estimation. They conclude that Boltzmann-code accuracy is now subdominant to recombination and foreground modeling uncertainties, with CLASS offering a robust framework for extending analyses beyond standard LambdaCDM.

Abstract

By confronting the two independent Boltzmann codes CLASS and CAMB, we establish that for concordance cosmology and for a given recombination history, lensed CMB and matter power spectra can be computed by current codes with an accuracy of 0.01%. We list a few tiny changes in CAMB which are necessary in order to reach such a level. Using the common limit of the two codes as a set of reference spectra, we derive precision settings corresponding to fixed levels of error in the computation of a CMB likelihood. We find that for a given precision level, CLASS is about 2.5 times faster than CAMB for computing the lensed CMB spectra of a LambdaCDM model. The nature of the main improvements in CLASS (which may each contribute to these performances) is discussed in companion papers.