We present $it{CosmoPower}$, a suite of neural cosmological power spectrum emulators providing orders-of-magnitude acceleration for parameter estimation from two-point statistics analyses of Large-Scale Structure (LSS) and Cosmic Microwave Background (CMB) surveys. The emulators replace the computation of matter and CMB power spectra from Boltzmann codes; thus, they do not need to be re-trained for different choices of astrophysical nuisance parameters or redshift distributions. The matter power spectrum emulation error is less than $0.4%$ in the wavenumber range $k in [10^{-5}, 10] , mathrm{Mpc}^{-1}$, for redshift $z in [0, 5]$. $it{CosmoPower}$ emulates CMB temperature, polarisation and lensing potential power spectra in the $5sigma$ region of parameter space around the $it{Planck}$ best fit values with an error $lesssim 20%$ of the expected shot noise for the forthcoming Simons Observatory. $it{CosmoPower}$ is showcased on a joint cosmic shear and galaxy clustering analysis from the Kilo-Degree Survey, as well as on a Stage IV $it{Euclid}$-like simulated cosmic shear analysis. For the CMB case, $it{CosmoPower}$ is tested on a $it{Planck}$ 2018 CMB temperature and polarisation analysis. The emulators always recover the fiducial cosmological constraints with differences in the posteriors smaller than sampling noise, while providing a speed-up factor up to $O(10^4)$ to the complete inference pipeline. This acceleration allows posterior distributions to be recovered in just a few seconds, as we demonstrate in the $it{Planck}$ likelihood case. $it{CosmoPower}$ is written entirely in Python, can be interfaced with all commonly used cosmological samplers and is publicly available https://github.com/alessiospuriomancini/cosmopower .
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