Uchuu N-body Simulation: Cosmological Insights

• Uchuu N-body simulation is a state-of-the-art cosmological computation that combines large volume and high mass resolution to track dark matter and substructure in detail.
• It employs advanced techniques such as 2LPTic initial conditions, ROCKSTAR halo finding, and SHAM/HOD modeling to generate high-fidelity mock galaxy catalogs for surveys like DESI and BOSS.
• Robust clustering analysis and accurate BAO feature resolution establish Uchuu as a critical benchmark for modeling cosmic structure and informing next-generation large-scale surveys.

The Uchuu N-body simulation is a state-of-the-art cosmological $N$-body computation designed to provide an unprecedented combination of large volume, mass resolution, and precise dark matter substructure tracking within the Planck flat-$\Lambda$CDM framework. Uchuu enables detailed modeling of cosmic structure formation and supports the creation of high-fidelity mock galaxy catalogs essential for contemporary and future large-scale structure (LSS) surveys, such as DESI and BOSS/eBOSS.

1. Simulation Architecture and Cosmological Foundation

The principal Uchuu run employs the GreeM massively parallel TreePM gravity solver, combining long-range Particle-Mesh (PM) with short-range tree algorithms. The simulation volume is a cube with a comoving side length $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$, corresponding to $V = 8\,h^{-3}\,\mathrm{Gpc}^3$ and containing $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$ dark matter particles. The individual particle mass is $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$, and the Plummer-equivalent gravitational softening length is $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$, delivering both large scale (BAO) coverage and robust halo resolution down to dwarf-galaxy masses (Ishiyama et al., 2020, Fernández-García et al., 2 Jul 2025).

These simulations adopt Planck-2015 cosmological parameters: $\Omega_m = 0.3089$, $\Omega_\Lambda = 0.6911$, $\Omega_b = 0.0486$, $\Lambda$0, $\Lambda$1, $\Lambda$2. Initial conditions are generated at $\Lambda$3 using 2LPTic (second-order Lagrangian perturbation theory) with CAMB transfer functions. Halos and subhalos are identified at 50 snapshots (from $\Lambda$4 to $\Lambda$5) using ROCKSTAR, with merger trees constructed via CONSISTENT-TREES (Prada et al., 2023, Ereza et al., 2023).

2. Dark Matter Clustering and Halo Substructure

Dark matter power spectra $\Lambda$6 are measured using multi-resolution folded mesh assignments to achieve $\Lambda$7 accuracy for $\Lambda$8 and $\Lambda$9 up to $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$0. BAO features at $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$1 are fully resolved. Comparisons with nonlinear fitting models (Smith & Angulo 2019, Mead et al. 2015) validate the simulation's fidelity from the linear to quasi-nonlinear regimes (Ishiyama et al., 2020).

The halo mass function $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$2 is measured for halos resolved with $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$3 particles, yielding $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$4. Residuals versus analytical forms (e.g., Despali et al. 2016) are $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$5 for $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$6 at $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$7. Subhalo mass functions exhibit $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$8 scaling for satellite fractions, with subhalo completeness $L_{\rm box} = 2\,h^{-1}\,\mathrm{Gpc}$9 for $V = 8\,h^{-3}\,\mathrm{Gpc}^3$0 (Ishiyama et al., 2020, Prada et al., 2023).

3. Mock Galaxy Catalogs and Lightcone Assembly

Uchuu provides the foundation for constructing high-fidelity mock catalogs via subhalo abundance matching (SHAM) and halo occupation distribution (HOD) modeling. The SHAM algorithm utilizes $V = 8\,h^{-3}\,\mathrm{Gpc}^3$1, the historical maximum of the circular velocity $V = 8\,h^{-3}\,\mathrm{Gpc}^3$2, as the matching variable. For mocks of DESI BGS-BRIGHT (rest-frame $V = 8\,h^{-3}\,\mathrm{Gpc}^3$3-band $V = 8\,h^{-3}\,\mathrm{Gpc}^3$4) and LRG ($V = 8\,h^{-3}\,\mathrm{Gpc}^3$5), a monotonic mapping is performed between the cumulative (sub)halo $V = 8\,h^{-3}\,\mathrm{Gpc}^3$6 distribution and the observed cumulative stellar mass or luminosity function, incorporating log-normal scatter to reflect galaxy-halo stochasticity.

The construction steps for lightcone mocks are:

• Layered shell assembly: The observer is placed at the origin of periodic box tilings. Lightcone shells use the nearest snapshot for each redshift bin (typical width $V = 8\,h^{-3}\,\mathrm{Gpc}^3$7 out to $V = 8\,h^{-3}\,\mathrm{Gpc}^3$8).
• Flux limits and completeness: BGS–BRIGHT mock galaxies are flux-limited to $V = 8\,h^{-3}\,\mathrm{Gpc}^3$9, and LRG mocks involve explicit removal of objects to match survey incompleteness.
• Color and magnitude modeling: SDSS $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$0 colors for BGS are assigned by a double-Gaussian evolution model; luminosities and stellar masses are $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$1-corrected to a reference $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$2.
• Survey footprint imposition: DESI Y1/Y3 and BOSS/eBOSS angular masks and selection functions are applied, with up to 8 cubes tiled for full-sky coverage.

Lightcone products allow direct clustering analysis matching survey geometry and selection criteria (Fernández-García et al., 2 Jul 2025, Ereza et al., 2023).

4. Clustering Analysis and Bias Calibration

Clustering is quantified using the Landy–Szalay estimator for the two-point correlation function $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$3, with multipoles $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$4 (monopole) and $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$5 (quadrupole) evaluated via Legendre projection, and configuration-space bins covering $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$6 (or $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$7 in BOSS/eBOSS), as well as corresponding Fourier-space power spectra $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$8 extending up to $N_p = 12\,800^3 \approx 2.10 \times 10^{12}$9 (pypower FFT estimator). Large-scale bias $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$0 is fit by matching the measured monopole in $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$1 to theory: $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$2 with $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$3 and $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$4 parameterized as a function of $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$5 or $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$6 thresholds.

Results demonstrate $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$7 agreement between Uchuu mocks and DESI data for $m_p = 3.27 \times 10^8\,h^{-1} M_\odot$8 (monopole), with robust recovery of clustering and bias dependencies on stellar mass, luminosity, and redshift. LRG quadrupole deviations at small scales ($m_p = 3.27 \times 10^8\,h^{-1} M_\odot$9) are attributed to velocity modeling limitations within SHAM. BAO features are well reproduced up to statistical errors (Fernández-García et al., 2 Jul 2025).

5. Covariance Estimation and Systematic Validation

To support robust cosmological inference, covariance matrices are constructed from thousands of GLAM-Uchuu lightcones, which use HODs directly measured from Uchuu SHAM catalogs. For each statistic (e.g., $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$0, $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$1), the empirical covariance is: $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$2 with rescaling for effective survey volume $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$3 if necessary. GLAM-Uchuu errors are shown to be more conservative on small scales than approximate methods (MD-Patchy, EZmock), which can underestimate diagonal errors by $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$4 for $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$5 (Ereza et al., 2023). This highlights the necessity of high-fidelity $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$6-body covariance for percent-level clustering analyses and systematic characterization.

6. Astrophysical Applications and Future Prospects

The Uchuu simulation underpins the reference mocks for DESI DR2, BOSS, and eBOSS, enabling full-shape BAO/RSD analyses, void statistics, and large-scale structure systematics studies. Publicly accessible data products include particle snapshots, halo/subhalo catalogs with $\epsilon = 4.27\,h^{-1}\,\mathrm{kpc}$7 and merger trees, mock lightcones, and strong/weak lensing maps (Ishiyama et al., 2020, Prada et al., 2023). Future data releases will expand to include semi-analytic galaxy catalogs as well as X-ray and AGN lightcones, leveraging Uchuu's unique volume and mass resolution.

A plausible implication is that Uchuu's combination of survey-scale volume and sub-kpc force resolution establishes a modern benchmark, surpassing previous simulations (Millennium, MultiDark, AbacusSummit, UNIT) in dynamic range, completeness, and systematic control. Its accuracy in reproducing LSS statistics across mass, luminosity, and redshift makes it a foundational resource for the statistical and systematic requirements of next-generation spectroscopic surveys (Ereza et al., 2023, Prada et al., 2023, Fernández-García et al., 2 Jul 2025).