A complete framework for cosmological emulation and inference with CosmoPower

We present a coherent, re-usable python framework which further builds on the cosmological emulator code CosmoPower. In the current era of high-precision cosmology, we require high-accuracy calculations of cosmological observables with Einstein-Boltzmann codes. For detailed statistical analyses, such codes often incur high costs in terms of computing power, making parameter space exploration costly, especially for beyond-$\Lambda$CDM analyses. Machine learning-enabled emulators of Einstein-Boltzmann codes have emerged as a solution to this problem and have become a common way to perform fast cosmological analyses. To enable generation, sharing and use of emulators for inference, we define standards for robustly describing, packaging and distributing them, and present software for easily performing these tasks in an automated and replicable manner. We provide examples and guidelines for generating your own sufficiently accurate emulators and wrappers for using them in popular cosmological inference codes. We demonstrate our framework by presenting a suite of high-accuracy emulators for the CAMB code's calculations of CMB $C_\ell$, $P(k)$, background evolution, and derived parameter quantities. We show that these emulators are accurate enough for both $\Lambda$CDM analysis and a set of single- and two-parameter extension models (including $N_{\rm eff}$, $\sum m_{\nu}$ and $w_0 w_a$ cosmologies) with stage-IV observatories, recovering the original high-accuracy Einstein-Boltzmann spectra to tolerances well within the cosmic variance uncertainties across the full range of parameters considered. We also use our emulators to recover cosmological parameters in a simulated cosmic-variance limited experiment, finding results well within $0.1 \sigma$ of the input cosmology, while requiring typically $\lesssim1/50$ of the evaluation time than for the full Einstein-Boltzmann computation.