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We investigate using three-point statistics in constraining the galaxy-halo connection. We show that for some galaxy samples, the constraints on the halo occupation distribution parameters are dominated by the three-point function signal (over its two-point counterpart). We demonstrate this on mock catalogues corresponding to the Luminous red galaxies (LRGs), Emission-line galaxies (ELGs), and quasars (QSOs) targeted by the Dark Energy Spectroscopic Instrument (DESI) Survey. The projected three-point function for triangle sides less up to 20 h-1 Mpc measured from a cubic Gpc of data can constrain the characteristic minimum mass of the LRGs with a preci sion of 0.46 per cent. For comparison, similar constraints from the projected two-point function are 1.55 per cent. The improvements for the ELGs and QSOs targets are more modest. In the case of the QSOs, it is caused by the high shot-noise of the sample, and in the case of the ELGs, it is caused by the range of halo masses of the host haloes. The most time-consuming part of our pipeline is the measurement of the three-point functions. We adopt a tabulation method, proposed in earlier works for the two-point function, to significantly reduce the required compute time for the three-point analysis.

Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N-body simulation codes, abacus, gadget-2, and swift, to investigate the regimes in which their results agree. We run N-body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109 h-1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for s > 20 h-1 Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109 h-1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than 20 h-1 Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10 h Mpc-1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-N-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy-halo relation will be presented in a follow-up study.

Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches ∼ 20 h-3, Gpc3. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with 200,-3}, Gpc3 (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-N-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. k < 0.3h Mpc-1 for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effective volume ∼20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

We present measurements of the redshift-dependent clustering of a DESI-like luminous red galaxy (LRG) sample selected from the Legacy Survey imaging data set, and use the halo occupation distribution (HOD) framework to fit the clustering signal. The photometric LRG sample in this study contains 2.7 million objects over the redshift range of 0.4 < z < 0.9 over 5655 deg2. We have developed new photometric redshift (photo-z) estimates using the Legacy Survey DECam and WISE photometry, with σNMAD = 0.02 precision for LRGs. We compute the projected correlation function using new methods that maximize signal-to-noise ratio while incorporating redshift uncertainties. We present a novel algorithm for dividing irregular survey geometries into equal-area patches for jackknife resampling. For a five-parameter HOD model fit using the MultiDark halo catalogue, we find that there is little evolution in HOD parameters except at the highest redshifts. The inferred large-scale structure bias is largely consistent with constant clustering amplitude over time. In an appendix, we explore limitations of Markov chain Monte Carlo fitting using stochastic likelihood estimates resulting from applying HOD methods to N-body catalogues, and present a new technique for finding best-fitting parameters in this situation. Accompanying this paper, we have released the Photometric Redshifts for the Legacy Surveys catalogue of photo-z's obtained by applying the methods used in this work to the full Legacy Survey Data Release 8 data set. This catalogue provides accurate photometric redshifts for objects with z < 21 over more than 16 000 deg2 of sky.

Galaxy–galaxy lensing (GGL) and clustering measurements from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) data set promise to yield unprecedented combined-probe tests of cosmology and the galaxy–halo connection. In such analyses, it is essential to identify and characterize all relevant statistical and systematic errors. We forecast the covariances of DESI Y1 GGL + clustering measurements and the systematic bias due to redshift evolution in the lens samples. Focusing on the projected clustering and GGL correlations, we compute a Gaussian analytical covariance, using a suite of N -body and lognormal simulations to characterize the effect of the survey footprint. Using the DESI one percent survey data, we measure the evolution of galaxy bias parameters for the DESI luminous red galaxy (LRG) and bright galaxy survey (BGS) samples. We find mild evolution in the LRGs in |$0.4 < z < 0.8$|⁠ , subdominant to the expected statistical errors. For BGS, we find less evolution for brighter absolute magnitude cuts, at the cost of reduced sample size. We find that for a redshift bin width |$\Delta z = 0.1$|⁠ , evolution effects on DESI Y1 GGL is negligible across all scales, all fiducial selection cuts, all fiducial redshift bins. Galaxy clustering is more sensitive to evolution due to the bias squared scaling. Nevertheless the redshift evolution effect is insignificant for clustering above the 1-halo scale of |$0.1h^{-1}$|  Mpc. For studies that wish to reliably access smaller scales, additional treatment of redshift evolution is likely needed. This study serves as a reference for GGL and clustering studies using the DESI Y1 sample. [ABSTRACT FROM AUTHOR]

We present the first comprehensive halo occupation distribution (HOD) analysis of the Dark Energy Spectroscopic Instrument (DESI) One-Percent Survey luminous red galaxy (LRG) and Quasi Stellar Object (QSO) samples. We constrain the HOD of each sample and test possible HOD extensions by fitting the redshift-space galaxy 2-point correlation functions in 0.15 < r < 32  h −1 Mpc in a set of fiducial redshift bins. We use AbacusSummit cubic boxes at Planck 2018 cosmology as model templates and forward model galaxy clustering with the AbacusHOD package. We achieve good fits with a standard HOD model with velocity bias, and we find no evidence for galaxy assembly bias or satellite profile modulation at the current level of statistical uncertainty. For LRGs in 0.4 < z < 0.6, we infer a satellite fraction of |$f_\mathrm{sat} = 11\pm 1~{y{\ \mathrm{per\,cent}}}$|⁠ , a mean halo mass of |$\log _{10}\overline{M}_h/M_\odot =13.40^{+0.02}_{-0.02}$|⁠ , and a linear bias of |$b_\mathrm{lin} = 1.93_{-0.04}^{+0.06}$|⁠. For LRGs in 0.6 < z < 0.8, we find |$f_\mathrm{sat}=14\pm 1~{{\ \mathrm{per\,cent}}}$|⁠ , |$\log _{10}\overline{M}_h/M_\odot =13.24^{+0.02}_{-0.02}$|⁠ , and |$b_\mathrm{lin}=2.08_{-0.03}^{+0.03}$|⁠. For QSOs, we infer |$f_\mathrm{sat}=3^{+8}_{-2}\mathrm{per\,cent}$|⁠ , |$\log _{10}\overline{M}_h/M_\odot = 12.65^{+0.09}_{-0.04}$|⁠ , and |$b_\mathrm{lin} = 2.63_{-0.26}^{+0.37}$| in redshift range 0.8 < z < 2.1. Using these fits, we generate a large suite of high fidelity galaxy mocks, forming the basis of systematic tests for DESI Y1 cosmological analyses. We also study the redshift-evolution of the DESI LRG sample from z  = 0.4 up to z  = 1.1, revealling significant and interesting trends in mean halo mass, linear bias, and satellite fraction. [ABSTRACT FROM AUTHOR]

Together with larger spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI), the precision of large-scale structure studies and thus the constraints on the cosmological parameters are rapidly improving. Therefore, one must build realistic simulations and robust covariance matrices. We build galaxy catalogues by applying a halo occupation distribution (HOD) model upon the FastPM simulations, such that the resulting galaxy clustering reproduces high-resolution N -body simulations. While the resolution and halo finder are different from the reference simulations, we reproduce the reference galaxy two-point clustering measurements – monopole and quadrupole – to a precision required by the DESI Year 1 emission line galaxy sample down to non-linear scales, i.e. |$k\lt 0.5\, h\, \mathrm{Mpc}^{-1}$| or |$s\gt 10\, \mathrm{Mpc}\, h^{-1}$|⁠. Furthermore, we compute covariance matrices based on the resulting FastPM galaxy clustering – monopole and quadrupole. We study for the first time the effect of fitting on Fourier conjugate (e.g. power spectrum) on the covariance matrix of the Fourier counterpart (e.g. correlation function). We estimate the uncertainties of the two parameters of a simple clustering model and observe a maximum variation of 20 per cent for the different covariance matrices. Nevertheless, for most studied scales the scatter is between 2 and 10  per cent. Consequently, using the current pipeline we can precisely reproduce the clustering of N -body simulations and the resulting covariance matrices provide robust uncertainty estimations against HOD fitting scenarios. We expect our methodology will be useful for the coming DESI data analyses and their extension for other studies. [ABSTRACT FROM AUTHOR]

Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N -body simulation codes, abacus , gadget-2 , and swift , to investigate the regimes in which their results agree. We run N -body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109  h −1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for |$s\ \gt\ 20\ h^{-1}$|  Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109  h −1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than |$20\ h^{-1}$|  Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10  h  Mpc−1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi- N -body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy–halo relation will be presented in a follow-up study. [ABSTRACT FROM AUTHOR]

Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches |$\sim 20\, h^{-3}\, \mathrm{Gpc}^{3}$|⁠. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with |$200\, h^{-3}\, \mathrm{Gpc}^{3}$| (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi- N -body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. |$k \lt 0.3\, h\, \mathrm{Mpc}^{-1}$| for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effective volume ∼20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data. [ABSTRACT FROM AUTHOR]