COMET: Clustering Observables Modelled by Emulated perturbation Theory

Abstract

In this paper we present COMET, a Gaussian process emulator of the galaxy power spectrum multipoles in redshift-space. The model predictions are based on one-loop perturbation theory and we consider two alternative descriptions of redshift-space distortions: one that performs a full expansion of the real-to redshift-space mapping, as in recent effective field theory models, and another that preserves the non-perturbative impact of small-scale velocities by means of an effective damping function. The outputs of COMET can be obtained at arbitrary redshifts (up to 𝑧 ∼ 3), for arbitrary fiducial background cosmologies, and for a large parameter space that covers the shape parameters 𝜔 𝑐 , 𝜔 𝑏 , and 𝑛 𝑠 , as well as the evolution parameters ℎ, 𝐴 𝑠 , Ω 𝐾 , 𝑤 0 , and 𝑤 𝑎 . This flexibility does not impair COMET's accuracy, since we exploit an exact degeneracy between the evolution parameters that allows us to train the emulator on a significantly reduced parameter space. While the predictions are sped up by at least two orders of magnitude, validation tests reveal an accuracy of 0.1 % for the monopole and quadrupole (0.3 % for the hexadecapole), or alternatively, better than 0.25 𝜎 for all three multipoles in comparison to statistical uncertainties expected for the Euclid survey with a tenfold increase in volume. We show that these differences translate into shifts in mean posterior values that are at most of the same size, meaning that COMET can be used with the same confidence as the exact underlying models. COMET is a publicly available Python package that also provides the tree-level bispectrum multipoles in redshift-space and Gaussian covariance matrices.

Window function convolution with deep neural network models

“…This is ideal for sampling posterior probabilities in Bayesian parameter estimation. Our method can be straightforwardly generalised to the multipoles of the spectra, and could also be combined with emulators that make predictions for the true clustering signal (including galaxy biasing) based on perturbation theory (e.g., Donald-McCann et al 2023;DeRose et al 2022;Eggemeier et al 2022). Additional corrections due to binning the theory predictions in exactly the same way as done for the measurements (see e.g., Sect.…”

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 ¶ Here, convergence means the change in the observed size of an object caused by gravitational lensing effect.…”

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.…”