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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>

Abstract:

Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the Rubin Observatory Legacy Survey of Space and Time (LSST) bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Year 10 (Y10) data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian perturbation theory (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. We consider a variety of different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of k_max = 0.4 Mpc^-1 for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data.

Abstract:

We present an emulator for the two-point clustering of biased tracers in real space. We construct this emulator using neural networks calibrated with more than 400 cosmological models in a 8D cosmological parameter space that includes massive neutrinos an dynamical dark energy. The properties of biased tracers are described via a Lagrangian perturbative bias expansion which is advected to Eulerian space using the displacement field of numerical simulations. The cosmology-dependence is captured thanks to a cosmology-rescaling algorithm. We show that our emulator is capable of describing the power spectrum of galaxy formation simulations for a sample mimicking that of a typical Emission-Line survey at z ∼1 with an accuracy of up to non-linear scales.

Abstract:

We present an emulator that accurately predicts the power spectrum of galaxies in redshift space as a function of cosmological parameters. Our emulator is based on a second-order Lagrangian bias expansion that is displaced to Eulerian space using cosmological N-body simulations. Redshift space distortions are then imprinted using the non-linear velocity field of simulated particles and haloes. We build the emulator using a forward neural network trained with the simulations of the BACCO project, which covers an eight-dimensional parameter space including massive neutrinos and dynamical dark energy. We show that our emulator provides unbiased cosmological constraints from the monopole, quadrupole, and hexadecapole of a mock galaxy catalogue that mimics the BOSS-CMASS sample down to non-linear scales (k ∼ 0.6hMpc^−1). This work opens up the possibility of robustly extracting cosmological information from small scales using observations of the large-scale structure of the universe.

Abstract:

The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift – the so-called concentration–mass–redshift relation, denoted c(M, z). We present here an extensive study of the cosmology-dependence of c(M, z) that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: σ8Mb, ns, h, Mν, w0, and wa. We characterize the impact of these parameters on concentrations for different halo masses and redshifts. In agreement with previous works, and for all cosmologies studied, we find that there exists a tight correlation between the characteristic densities of dark matter haloes within their scale radii, r−2, and the critical density of the universe at a suitably defined formation time. This finding, when combined with excursion set modelling of halo formation histories, allows us to accurately predict the concentrations of dark matter haloes as a function of mass, redshift, and cosmology. We use our simulations to test the reliability of a number of published models for predicting halo concentration and highlight when they succeed or fail to reproduce the cosmological c(M, z) relation.