Nonlinear perturbation theory extension of the Boltzmann code CLASS

Abstract

We present a new open-source code that calculates one-loop power spectra and cross spectra for matter fields and biased tracers in real and redshift space. These spectra incorporate all ingredients required for a direct application to data: nonlinear bias and redshift-space distortions, infrared resummation, counterterms, and the Alcock-Paczynski effect. Our code is based on the Boltzmann solver CLASS and inherits its advantageous properties: user friendliness, ease of modification, high speed, and simple interface with other software. We present detailed descriptions of the theoretical model, the code structure, approximations, and accuracy tests. A typical end-to-end run for one cosmology takes 0.3 seconds, which is sufficient for Markov chain Monte Carlo parameter extraction. As an example, we apply the code to the Baryon Oscillation Spectroscopic Survey (BOSS) data and infer cosmological parameters from the shape of the galaxy power spectrum.

Constraining early dark energy with large-scale structure

“…It is worth mentioning that the oscillating residual observed in Fig. 4 is larger than the numerical inaccuracies of the CLASS-PT code, which do not exceed the 0.1% level [53]. It was shown in Ref.…”

“…Various ingredients of this approach (e.g., UV counterterms and IR resummation) have been independently derived in many different setups. Second, there was significant improvement in numerical methods, which allowed one to build extensions of standard Boltzmann codes that consistently calculate the nonlinear galaxy clustering observables as a function of cosmological parameters [52,53]. 5 Exploiting all these results, we show that the shape information in the galaxy power spectrum is important and that the new BOSS likelihood used in our analysis indeed leads to much stronger constraints on EDE compared to the standard BOSS likelihood.…”

“…[20] (see also Refs. [21,53] and references therein for more detail about theoretical modelling and the EFT approach). 6 It is instructive to look at the effects of the EDE on the observed redshift-space galaxy power spectrum.…”

“…In the following, we use a combined Einstein-Boltzmann code comprised of CLASS_EDE [40] and CLASS-PT [53] (both extensions of CLASS [70]), interfaced with the Monte Carlo sampling code MONTE PYTHON [71,72]. Each of these codes is publicly available.…”

“…We refer the reader to Refs. [20,53] for details of the pre-reconstruction full-shape galaxy power spectrum likelihood (based on the EFT described earlier) and to Ref. [23] for details of the post-reconstruction BAO extraction and the BAO-FS covariance matrix.…”