COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys

TL;DR

CosmoPower delivers neural-network emulators for both LSS and CMB power spectra, replacing computationally intensive Boltzmann solvers to enable rapid Bayesian inference for current and upcoming surveys. By using direct NN and PCA-based strategies, trained over broad parameter ranges and integrated with standard samplers, it achieves up to ~10^4–10^5x speed-ups while maintaining unbiased cosmological constraints as validated on KiDS, Euclid-like, and Planck analyses. The work demonstrates strong end-to-end applicability, differentiability, and GPU scalability, with plans to extend to higher-order statistics and beyond-LCDM cosmologies. Publicly available and designed to operate train-once-use-repeatedly, CosmoPower stands to substantially boost the scientific return of Stage IV cosmology analyses.

Abstract

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 $5σ$ region of parameter space around the $\it{Planck}$ best fit values with an error $\lesssim 10\%$ 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 at https://github.com/alessiospuriomancini/cosmopower .

Figures (8)

• Figure 2: Matter power spectrum emulation accuracy for a) the linear power spectrum and b) the nonlinear correction, as measured on the $\sim 2 \cdot 10^4$ spectra of the testing set for our emulators. Dark red, red and salmon areas enclose the 68, 95 and 99 percentiles of the fractional absolute emulator error, respectively, as a function of wavenumber $k$. By construction, the redshift $z$ is an input parameter for the emulators. Therefore, these percentile curves are computed with spectra evaluated at redshifts $z \in [0, 5]$, i.e. spanning the whole range of validity of our emulators.
• Figure 3: Contours for the 3x2pt analysis of the KiDS-450 and GAMA surveys. In red contours obtained with Class, in blue those obtained with CosmoPower.
• Figure 4: Contours for a simulated cosmic shear analysis of a Euclid-like Stage IV surveys. In red contours obtained with Class, in blue those obtained with CosmoPower.
• Figure 5: CMB power spectra emulation accuracy on the 5$\sigma$ range test set for a) the temperature power spectrum, b) the polarisation power spectrum, c) the temperature-polarisation cross power spectrum, d) the lensing potential power spectrum. The emulation error is defined with respect to both instrumental and statistical noise, and is defined in Eqs. (\ref{['eq:cl_cmb_error']}-\ref{['eq:cl_cmb_error_te']}). Dark red, red and salmon areas enclose the 68, 95 and 99 percentiles of the test set. Details of the neural models are reported in Appendix \ref{['app:nn']}.
• Figure 6: Planck 2018 3x2pt analysis considering $C_{\ell}^{\textrm{TT}}$, $C_{\ell}^{\textrm{EE}}$ and $C_{\ell}^{\textrm{TE}}$. The red contours are obtained in $\sim 1.2 \cdot 10^5$ seconds on 80 CPU cores using Class, while the blue contours take roughly 10 seconds on a single GPU using our neural emulators. Note that the constraints on $100 \theta_{\textrm{S}}$ are derived from the rest of the samples using a Gaussian Process.