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

We present Capse.jl, a novel emulator that utilizes neural networks to predict 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 planned CMB-S4 survey. Capse.jl can also be trained in an hour's time on a CPU. As a test case, we use Capse.jl to analyze Planck 2018 data and ACT DR4 data. We obtain the same result as standard analysis methods with a computational efficiency 3 to 6 order of magnitude higher. We take advantage of the differentiability of our emulators to use gradients-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 Planck 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.