SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrum
Astronomy & Astrophysics EDP Sciences 686 (2024) ARTN A150
Abstract:
<jats:p><jats:italic>Context.</jats:italic>Rapid and accurate evaluation of the nonlinear matter power spectrum,<jats:italic>P</jats:italic>(<jats:italic>k</jats:italic>), as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators.</jats:p><jats:p><jats:italic>Aims.</jats:italic>We aim to accelerate symbolic approximations to<jats:italic>P</jats:italic>(<jats:italic>k</jats:italic>) by removing the requirement to perform integrals, instead using short symbolic expressions to compute all variables of interest. We also wish to make such expressions more accurate by re-optimising the parameters of these models (using a larger number of cosmologies and focussing on cosmological parameters of more interest for present-day studies) and providing correction terms.</jats:p><jats:p><jats:italic>Methods.</jats:italic>We use symbolic regression to obtain simple analytic approximations to the nonlinear scale,<jats:italic>k</jats:italic><jats:sub><jats:italic>σ</jats:italic></jats:sub>, the effective spectral index,<jats:italic>n</jats:italic><jats:sub>eff</jats:sub>, and the curvature,<jats:italic>C</jats:italic>, which are required for the<jats:sc>HALOFIT</jats:sc>model. We then re-optimise the coefficients of<jats:sc>HALOFIT</jats:sc>to fit a wide range of cosmologies and redshifts. We then again exploit symbolic regression to explore the space of analytic expressions to fit the residuals between<jats:italic>P</jats:italic>(<jats:italic>k</jats:italic>) and the optimised predictions of<jats:sc>HALOFIT</jats:sc>. Our results are designed to match the predictions of<jats:sc>EUCLIDEMULATOR</jats:sc>2, but we validate our methods against<jats:italic>N</jats:italic>-body simulations.</jats:p><jats:p><jats:italic>Results.</jats:italic>We find symbolic expressions for<jats:italic>k</jats:italic><jats:sub><jats:italic>σ</jats:italic></jats:sub>,<jats:italic>n</jats:italic><jats:sub>eff</jats:sub>and<jats:italic>C</jats:italic>which have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. We provide re-optimised<jats:sc>HALOFIT</jats:sc>parameters, which reduce the root mean squared fractional error (compared to<jats:sc>EUCLIDEMULATOR</jats:sc>2) from 3% to below 2% for wavenumbers<jats:italic>k</jats:italic> = 9 × 10<jats:sup>−3</jats:sup> − 9 <jats:italic>h</jats:italic> Mpc<jats:sup>−1</jats:sup>. We introduce<jats:sc>SYREN-HALOFIT</jats:sc>(symbolic-regression-enhanced<jats:sc>HALOFIT</jats:sc>), an extension to<jats:sc>HALOFIT</jats:sc>containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current<jats:sc>HALOFIT</jats:sc>and<jats:sc>HMCODE</jats:sc>implementations, respectively, and 2680 and 64 times faster than<jats:sc>EUCLIDEMULATOR</jats:sc>2 (which requires running<jats:sc>CLASS</jats:sc>) and the<jats:sc>BACCO</jats:sc>emulator. We obtain comparable accuracy to<jats:sc>EUCLIDEMULATOR</jats:sc>2 and the<jats:sc>BACCO</jats:sc>emulator when tested on<jats:italic>N</jats:italic>-body simulations.</jats:p><jats:p><jats:italic>Conclusions.</jats:italic>Our work greatly increases the speed and accuracy of symbolic approximations to<jats:italic>P</jats:italic>(<jats:italic>k</jats:italic>), making them significantly faster than their numerical counterparts without loss of accuracy.</jats:p>The effect of wave dark matter on equal mass black hole mergers
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