SYREN-NEW: Precise formulae for the linear and nonlinear matter power spectra with massive neutrinos and dynamical dark energy

¹ Department of Astronomy, Tsinghua University, Beijing 100084, China
² CNRS & Sorbonne Université, Institut d’Astrophysique de Paris (IAP), UMR 7095, 98 bis bd Arago, F-75014 Paris, France
³ Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
⁴ Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX, UK
⁵ Astrophysics, University of Oxford, Keble Road, OX1 3RH, UK
⁶ Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA
⁷ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

^⋆ Corresponding authors: suic20@mails.tsinghua.edu.cn, deaglan.bartlett@iap.fr

Received: 3 November 2024
Accepted: 24 February 2025

Abstract

Context. Current and future large-scale structure surveys aim to constrain the neutrino mass and the equation of state of dark energy. To do this efficiently, rapid yet accurate evaluation of the matter power spectrum in the presence of these effects is essential.

Aims. We aim to construct accurate and interpretable symbolic approximations of the linear and nonlinear matter power spectra as a function of cosmological parameters in extended ΛCDM models that contain massive neutrinos and nonconstant equations of state for dark energy. This constitutes an extension of the SYREN-HALOFIT emulators to incorporate these two effects, which we call SYREN-NEW (SYmbolic-Regression-ENhanced power spectrum emulator with NEutrinos and W₀−w_a). We also wish to obtain a simple approximation of the derived parameter, σ₈, as a function of the cosmological parameters for these models.

Methods. We utilizedd symbolic regression to efficiently search through candidate analytic expressions to approximate the various quantities of interest. Our results for the linear power spectrum are designed to emulate CLASS, whereas for the nonlinear case we aim to match the results of EUCLIDEMULATOR2. We compared our results to existing emulators and N-body simulations.

Results. Our analytic emulators for σ₈, and the linear and nonlinear power spectra achieve root mean squared errors of 0.1%, 0.3%, and 1.3%, respectively, across a wide range of cosmological parameters, redshifts and wavenumbers. The error on the nonlinear power spectrum is reduced by approximately a factor of 2 when considering observationally plausible dark energy models and neutrino masses. We verify that emulator-related discrepancies are subdominant compared to observational errors and other modeling uncertainties when computing shear power spectra for LSST-like surveys. Our expressions have similar accuracy to existing (numerical) emulators, but are at least an order of magnitude faster, both on a CPU and a GPU.

Conclusions. Our work greatly improves the accuracy, speed, and applicability range of current symbolic approximations of the linear and nonlinear matter power spectra. These now cover the same range of cosmological models as many numerical emulators with similar accuracy, but are much faster and more interpretable. We provide publicly available code for all symbolic approximations found.