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We present the data release of the Uchuu-SDSS galaxies: a set of 32 high-fidelity galaxy lightcones constructed from the large Uchuu 2.1 trillion particle $N$-body simulation using Planck cosmology. We adopt subhalo abundance matching to populate the Uchuu-box halo catalogues with SDSS galaxy luminosities. These cubic box galaxy catalogues generated at several redshifts are combined to create the set of lightcones with redshift-evolving galaxy properties. The Uchuu-SDSS galaxy lightcones are built to reproduce the footprint and statistical properties of the SDSS main galaxy survey, along with stellar masses and star formation rates. This facilitates direct comparison of the observed SDSS and simulated Uchuu-SDSS data. Our lightcones reproduce a large number of observational results, such as the distribution of galaxy properties, the galaxy clustering, the stellar mass functions, and the halo occupation distributions. Using the simulated and real data we select samples of bright red galaxies at $z_\mathrm{eff}=0.15$ to explore Redshift Space Distortions and Baryon Acoustic Oscillations (BAO) utilizing a full-shape analytical model of the two-point correlation function. We create a set of 5100 galaxy lightcones using GLAM N-body simulations to compute covariance errors. We report a $\sim 30\%$ precision increase on $f\sigma_8$, due to our better estimate of the covariance matrix. From our BAO-inferred $\alpha_{\parallel}$ and $\alpha_{\perp}$ parameters, we obtain the first SDSS measurements of the Hubble and angular diameter distances $D_\mathrm{H}(z=0.15) / r_d = 27.9^{+3.1}_{-2.7}$, $D_\mathrm{M}(z=0.15) / r_d = 5.1^{+0.4}_{-0.4}$. Overall, we conclude that the Planck LCDM cosmology nicely explains the observed large-scale structure statistics of SDSS. All data sets are made publicly available., Comment: 20 Pages, Submitted to MNRAS

Measurements of the luminosity function of active galactic nuclei (AGN) at high redshift ($z\gtrsim 6$) are expected to suffer from field-to-field variance, including cosmic and Poisson variances. Future surveys, such as those from the Euclid telescope and James Webb Space Telescope (JWST), will also be affected by field variance. We use the Uchuu simulation, a state-of-the-art cosmological $N$-body simulation with 2.1 trillion particles in a volume of $25.7~\mathrm{Gpc}^3$, that has sufficient mass resolution to resolve dwarf-size systems, combined with a semi-analytic galaxy and AGN formation model, to generate the Uchuu-$\nu^2$GC catalog, publicly available, that allows us to investigate the field-to-field variance of the luminosity function of AGN. With this Uchuu-$\nu^2$GC model, we quantify the cosmic variance as a function of survey area, AGN luminosity, and redshift. In general, cosmic variance decreases with increasing survey area and decreasing redshift. We find that at $z\sim6-7$, the cosmic variance depends weakly on AGN luminosity, in particular for small survey areas (0.01 and 0.1 deg$^2$). This is because the typical mass of dark matter haloes in which AGN reside does not significantly depend on luminosity. Due to the rarity of AGN, Poisson variance dominates the total field-to-field variance, especially for bright AGN. We discuss uncertainties present in the estimation of the faint-end of the AGN luminosity function from recent observations, and extend this to make predictions for the expected number of AGN and their variance for upcoming observations with Euclid, JWST, and the Legacy Survey of Space and Time (LSST). In particular, we predict that the Euclid deep survey will find 120--240 (16--80) AGN -- depending on the model -- with rest-frame UV absolute magnitude brighter than $-20$ ($-20.5$) at $z=6.3$ ($z=7$) in the Euclid H-band deep survey (abridged)., Comment: 17 pages, 17 figures, submitted to MNRAS, corrected the following link, All Uchuu-$\nu^2$GC data used for this paper is publicly available in our Skies & Universes website http://skiesanduniverses.org/Simulations/Uchuu/