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

Abstract

The 3D matter power spectrum, P δ (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, ∆P δ /P δ centered on 0. It is also ∼ 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 (emuPK) can be trained with any set of points and is distributed on Github, and comes with 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.

The growth of density perturbations in the last ∼10 billion years from tomographic large-scale structure data

“…as a polynomial in z or a) or, more ideally, modelling it as a Gaussian process with its hyperparameters and conditional distribution determined from the data. Existing off-the-shelf parameter inference frameworks for the cosmological analysis of large-scale structure data are not efficient enough yet to deal with the high-dimensional parameter spaces associated with Gaussian processes (although the community is moving fast in that direction [35,36]), and therefore we choose a middle ground. In our case, D(z) is determined by its value at a set of fixed redshift nodes Dz i ≡ D(z i ).…”

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

“…The matter power spectrum emulators built from the Coyote Universe simulations (Heitmann et al 2009(Heitmann et al , 2010(Heitmann et al , 2013Lawrence et al 2010a;Lawrence et al 2010bLawrence et al , 2017 are based on Gaussian Process regression (Rasmussen & Williams 2005), and were extended by Ramachandra et al (2020) to 𝑓 (𝑅) cosmologies. Recently, the Euclid Emulator was proposed as a surrogate model for the nonlinear matter power spectrum (Knabenhans et al 2019;Euclid Collaboration et al 2020a), Mootoovaloo et al (2020) developed a Gaussian Process emulator of cosmic shear band powers, while Mootoovaloo et al (2021) and Ho et al (2021) used Gaussian Processes to emulate the matter power spectrum. Bird et al (2019) and Rogers et al (2019) developed Gaussian Process emulators for the Lyman-𝛼 forest flux power spectrum.…”

$\texttt{matryoshka}$: Halo Model Emulator for the Galaxy Power Spectrum

“…The prediction of the boost coming from the emulator is generally orders of magnitude faster than the linear theory prediction. Several recent works have applied the idea of emulation to predictions coming from linear theory (Aricò et al 2021;Mootoovaloo et al 2021;Mancini et al 2021). These linear theory emulators have uses beyond the boosting method mentioned above as they can also be used to speed up any cosmological analysis that requires a linear theory prediction for the power spectrum.…”