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

Abstract

We present 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 $0.4{{\ \rm per\ cent}}$ in the wavenumber range k ∈ [10−5, 10] Mpc−1, for redshift z ∈ [0, 5]. CosmoPower emulates CMB temperature, polarisation and lensing potential power spectra in the 5σ region of parameter space around the Planck best fit values with an error $\lesssim 10{{\ \rm per\ cent}}$ of the expected shot noise for the forthcoming Simons Observatory. CosmoPower is showcased on a joint cosmic shear and galaxy clustering analysis from the Kilo-Degree Survey, as well as on a Stage IV Euclid-like simulated cosmic shear analysis. For the CMB case, CosmoPower is tested on a 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(104) to the complete inference pipeline. This acceleration allows posterior distributions to be recovered in just a few seconds, as we demonstrate in the Planck likelihood case. CosmoPower is written entirely in Python, can be interfaced with all commonly used cosmological samplers and is publicly available.

class_sz I: Overview

“…[12], building on previous work from Ref. [13]. This allows class_sz to predict these spectra in less than 50 ms, compared to around a minute if the calculations were to be done with class for the same accuracy requirements.…”

Machine learning for observational cosmology

“…We list large-scale cosmological simulation projects for emulators that interpolate summary statistics measured from simulations over the cosmological parameter space in table 1. We note also that there are many other attempts to utilize emulators for different purposes, such as developing fast Boltzmann equation solvers or performing low-order perturbative calculations [323][324][325][326][327][328][329][330][331][332][333][334][335][336], to explore the galaxy-halo connection for fixed cosmology [337], to translate less costly, low-resolution simulations to mimic more expensive simulations. More specifically, the applications include incorporating baryonic effects to the dark-matter only simulations [338], predicting Lyman-α forest [339,340] or 21 cm power spectra [341,342], extrapolating the predictions in Λ-cold dark matter (CDM) cosmology to alternative cosmological models Table 1.…”

Cosmology-informed neural networks to solve the background dynamics of the Universe

“…with the initial condition u 0 ðθÞ. If we consider the special case where the function fðt; θÞ can be expressed as fðt; θÞ ¼ P Q i h i ðθÞg i ðtÞ, 4 the general solution to Eq. ( 40) is…”

“…For example, in Ref. [4] ANNs were trained through supervised learning on the outputs of a numerical method to constrain the Lambda cold dark matter (ΛCDM) model with cosmic microwave background (CMB) and large-scale structure data. Also, ANNs trained through unsupervised learning were used to compute the tunneling profiles of cosmological phase transitions in Ref.…”