CLASS_SZ II: Notes and Examples of Fast and Accurate Calculations of Halo Model, Large Scale Structure and Cosmic Microwave Background Observables

These notes are very much work-in-progress and simply intended to showcase, in various degrees of details (and rigour), some of the cosmology calculations that class_sz can do. We describe the class_sz code in C, Python and Jax. Based on the Boltzmann code class, it can compute a wide range of observables relevant to current and forthcoming CMB and Large Scale Structure surveys. This includes galaxy shear and clustering, CMB lensing, thermal and kinetic Sunyaev and Zeldovich observables, Cosmic Infrared Background, cross-correlations and three-point statistics. Calculations can be done either within the halo model or the linear bias model. For standard $\Lambda$CDM cosmology and extensions, class_sz uses high-accuracy cosmopower emulators of the CMB and matter power spectrum to accelerate calculations. With this, along with efficient numerical integration routines, most class_sz output can be obtained in less than 500 ms (CMB $C_\ell$'s or matter $P(k)$ take $\mathcal{O}(1\mathrm{ms})$), allowing for fast or ultra-fast parameter inference analyses. Parts of the calculations are "jaxified", so the software can be integrated into differentiable pipelines.