Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS

Abstract

The 3D matter power spectrum, $P_{\delta }(k,z)$ is a fundamental quantity in the analysis of cosmological data such as large-scale structure, 21cm observations, and weak lensing. Existing computer models (Boltzmann codes) such as CLASS can provide it at the expense of immoderate computational cost. In this paper, we propose a fast Bayesian method to generate the 3D matter power spectrum, for a given set of wavenumbers, $k$ and redshifts, $z$. Our code allows one to calculate the following quantities: the linear matter power spectrum at a given redshift (the default is set to 0); the non-linear 3D matter power spectrum with/without baryon feedback; the weak lensing power spectrum. The gradient of the 3D matter power spectrum with respect to the input cosmological parameters is also returned and this is useful for Hamiltonian Monte Carlo samplers. The derivatives are also useful for Fisher matrix calculations. In our application, the emulator is accurate when evaluated at a set of cosmological parameters, drawn from the prior, with the fractional uncertainty, $\Delta P_{\delta }/P_{\delta }$ centred on 0. It is also $\sim 300$ times faster compared to CLASS, hence making the emulator amenable to sampling cosmological and nuisance parameters in a Monte Carlo routine. In addition, once the 3D matter power spectrum is calculated, it can be used with a specific redshift distribution, $n(z)$ to calculate the weak lensing and intrinsic alignment power spectra, which can then be used to derive constraints on cosmological parameters in a weak lensing data analysis problem. The software ($\text{emuPK}$) can be trained with any set of points and is distributed on Github, and comes with a pre-trained set of Gaussian Process (GP) models, based on 1000 Latin Hypercube (LH) samples, which follow roughly the current priors for current weak lensing analyses.

arXiv comment14 pages, 10 figures, Accepted for publication in Astronomy and Computing Journal

References in corpus (36)

• Bayes in the sky: Bayesian inference and model selection in cosmology
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics
• On the Complexity of Best Arm Identification in Multi-Armed Bandit Models
• Extended Limber Approximation
• The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum
• Calibrating Redshift Distributions Beyond Spectroscopic Limits with Cross-Correlations
• Massive Lossless Data Compression and Multiple Parameter Estimation from Galaxy Spectra
• The Coyote Universe II: Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
• The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum
• Fast likelihood-free cosmology with neural density estimators and active learning
• Estimating the Redshift Distribution of Faint Galaxy Samples
• KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters
• The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum
• Measuring the effective complexity of cosmological models
• Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
• Redshift distributions of galaxies in the DES Science Verification shear catalogue and implications for weak lensing
• Cosmic Calibration: Constraints from the Matter Power Spectrum and the Cosmic Microwave Background
• Nuisance hardened data compression for fast likelihood-free inference
• Baryons, Neutrinos, Feedback and Weak Gravitational Lensing
• Automatic physical inference with information maximising neural networks
• Emulation of reionization simulations for Bayesian inference of astrophysics parameters using neural networks
• Fast cosmological parameter estimation using neural networks
• Bayesian optimisation for likelihood-free cosmological inference
• H_0 and Odds on Cosmology
• Accurate emulator for the redshift-space power spectrum of dark matter halos and its application to galaxy power spectrum
• Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
• PkANN - II. A non-linear matter power spectrum interpolator developed using artificial neural networks
• PkANN - I. Non-linear matter power spectrum interpolation through artificial neural networks
• Euclid-era cosmology for everyone: Neural net assisted MCMC sampling for the joint 3x2 likelihood
• CosmicNet I: Physics-driven implementation of neural networks within Boltzmann-Einstein solvers
• Parameter Inference for Weak Lensing using Gaussian Processes and MOPED
• Intelligent Design: On the Emulation of Cosmological Simulations
• Primordial power spectrum and cosmology from black-box galaxy surveys
• Weak lensing reconstructions in 2D & 3D: implications for cluster studies
• Pico: Parameters for the Impatient Cosmologist

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• syren-halofit: A fast, interpretable, high-precision formula for the $\Lambda$CDM nonlinear matter power spectrum
• Fast and robust Bayesian Inference using Gaussian Processes with GPry
• LINNA: Likelihood Inference Neural Network Accelerator
• KiDS-1000 Cosmology: machine learning -- accelerated constraints on Interacting Dark Energy with COSMOPOWER
• A precise symbolic emulator of the linear matter power spectrum
• syren-new: Precise formulae for the linear and nonlinear matter power spectra with massive neutrinos and dynamical dark energy
• Accelerating cosmological inference with Gaussian processes and neural networks -- an application to LSST Y1 weak lensing and galaxy clustering
• LimberJack.jl: auto-differentiable methods for angular power spectra analyses
• Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning
• Cosmological gravity on all scales IV: 3x2pt Fisher forecasts for pixelised phenomenological modified gravity
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