High-accuracy emulators for observables in $\Lambda$CDM, $N_\mathrm{eff}$, $\Sigma m_\nu$, and $w$ cosmologies

We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the Cosmic Microwave Background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein-Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including $\Lambda$CDM, $w$CDM, $\Lambda$CDM+$N_\mathrm{eff}$, and $\Lambda$CDM+$\Sigma m_\nu$. Our CMB emulators are accurate to better than 0.5% out to $\ell=10^4$ which is sufficient for Stage-IV data analysis, and our $P(k)$ emulators reach the same accuracy level out to $k=50 \,\, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository CosmoPower Organisation, which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to CLASS and CAMB and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.