We present large-scale structure catalogs from the completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). Derived from Sloan Digital Sky Survey (SDSS) -IV Data Release 16 (DR16), these catalogs provide the data samples, corrected for observational systematics, and random positions sampling the survey selection function. Combined, they allow large-scale clustering measurements suitable for testing cosmological models. We describe the methods used to create these catalogs for the eBOSS DR16 Luminous Red Galaxy (LRG) and Quasar samples. The quasar catalog contains 343,708 redshifts with 0.8 < z < 2.2 over 4,808 deg2. We combine 174,816 eBOSS LRG redshifts over 4,242 deg2 in the redshift interval 0.6 < z < 1.0 with SDSS-III BOSS LRGs in the same redshift range to produce a combined sample of 377,458 galaxy redshifts distributed over 9,493 deg2. Improved algorithms for estimating redshifts allow that 98 per cent of LRG observations result in a successful redshift, with less than one per cent catastrophic failures (Δz > 1000 km s−1). For quasars, these rates are 95 and 2 per cent (with Δz > 3000 km s−1). We apply corrections for trends between the number densities of our samples and the properties of the imaging and spectroscopic data. For example, the quasar catalog obtains a χ2/DoF=776/10 for a null test against imaging depth before corrections and a χ2/DoF=6/8 after. The catalogs, combined with careful consideration of the details of their construction found here-in, allow companion papers to present cosmological results with negligible impact from observational systematic uncertainties.

We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$ by estimating the statistic EG, a probe of gravity, on cosmological scales 19 − 190 h−1Mpc. This is the highest-redshift and largest-scale estimation of EG so far. We use the quasar sample with redshifts 0.8 < z < 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_\ell ^{qq}$ and the redshift-space distortion (RSD) parameter β are estimated. By cross correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_\ell ^{\kappa q}$ signal at 12 σ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at 5 bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at 1 σ level over all these scales. With the CM estimated with 300 simulations, we report a best-fit scale-averaged estimate of $E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm GR}(\bar{z})=0.33$ with Planck 2018 CMB+BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.

Line-intensity mapping (LIM) is a promising technique to constrain the global distribution of galaxy properties. To combine LIM experiments probing different tracers with traditional galaxy surveys and fully exploit the scientific potential of these observations, it is necessary to have a physically motivated modeling framework. As part of developing such a framework, in this work, we introduce and model the conditional galaxy property distribution (CGPD), i.e., the distribution of galaxy properties conditioned on the host halo mass and redshift. We consider five galaxy properties, including the galaxy stellar mass, molecular gas mass, galaxy radius, gas-phase metallicity, and star formation rate (SFR), which are important for predicting the emission lines of interest. The CGPD represents the full distribution of galaxies in the five-dimensional property space; many important galaxy distribution functions and scaling relations, such as the stellar mass function and SFR main sequence, can be derived from integrating and projecting it. We utilize two different kinds of cosmological galaxy simulations, a semi-analytic model and the IllustrisTNG hydrodynamic simulation, to characterize the CGPD and explore how well it can be represented using a Gaussian mixture model (GMM). We find that with just a few (approximately three) Gaussian components, a GMM can describe the CGPD of the simulated galaxies to high accuracy for both simulations. The CGPD can be mapped to LIM or other observables by constructing the appropriate relationship between galaxy properties and the relevant observable tracers, which will be discussed in future works.

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