Capse.jl: efficient and auto-differentiable CMB power spectra emulation

We present Capse.jl, a novel neural network-based emulator designed for rapid and accurate prediction of Cosmic Microwave Background (CMB) temperature, polarization, and lensing angular power spectra. The emulator computes predictions in just a few microseconds with emulation errors below $0.1\sigma$ for all the scales relevant for the upcoming CMB-S4 survey. Capse.jl can also be trained in an hour's time on a 8-cores CPU. We test Capse.jl on Planck 2018, ACT DR4, and 2018 SPT-3G data and demonstrate its capability to derive cosmological constraints comparable to those obtained by traditional methods, but with a computational efficiency that is three to six orders of magnitude higher. We take advantage of the differentiability of our emulators to use gradient-based methods, such as Pathfinder and Hamiltonian Monte Carlo (HMC), which speed up the convergence and increase sampling efficiency. Together, these features make Capse.jl a powerful tool for studying the CMB and its implications for cosmology. When using the fastest combination of our likelihoods, emulators, and analysis algorithm, we are able to perform a Plancky TT + TE + EE analysis in less than a second. To ensure full reproducibility, we provide open access to the codes and data required to reproduce all the results of this work.