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: $\Omega_m = 0.3089$, $\Omega_\Lambda = 0.6911$, $\Omega_b = 0.0486$, $h = 0.6774$, $n_s = 0.9667$, $\sigma_8 = 0.8159$. Initial conditions are generated at $z_{\rm init}=127$ using 2LPTic (second-order Lagrangian perturbation theory) with CAMB transfer functions. Halos and subhalos are identified at 50 snapshots (from $z=14$ to $z=0$) 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 $P(k)$ are measured using multi-resolution folded mesh assignments to achieve $<1\%$ accuracy for $k<1\,h\,\mathrm{Mpc}^{-1}$ and $<3\%$ up to $k=10\,h\,\mathrm{Mpc}^{-1}$. BAO features at $k\sim0.07, 0.13\,h\,\mathrm{Mpc}^{-1}$ 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 $dn/dM$ is measured for halos resolved with $\geq40$ particles, yielding $M_{\rm vir}\geq 1.3\times10^{10}\,M_\odot/h$. Residuals versus analytical forms (e.g., Despali et al. 2016) are $\lesssim5\%$ for $10^{11}-3\times10^{14}\,M_\odot/h$ at $z=0$. Subhalo mass functions exhibit $N(>\mu)\propto\mu^{-0.75}$ scaling for satellite fractions, with subhalo completeness $>90\%$ for $V_{\rm peak}\gtrsim70\,\mathrm{km\,s^{-1}}$ (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 $V_{\rm peak}$, the historical maximum of the circular velocity $V_{\rm max}(t)$, as the matching variable. For mocks of DESI BGS-BRIGHT (rest-frame $r$-band $M_r$) and LRG ($\log M_\star$), a monotonic mapping is performed between the cumulative (sub)halo $V_{\rm peak}$ 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 $\Delta z = 0.05$ out to $z=1.1$).
• Flux limits and completeness: BGS–BRIGHT mock galaxies are flux-limited to $r<19.5$, and LRG mocks involve explicit removal of objects to match survey incompleteness.
• Color and magnitude modeling: SDSS $g-r$ colors for BGS are assigned by a double-Gaussian evolution model; luminosities and stellar masses are $k+E$-corrected to a reference $z$.
• 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 $\xi(s, \mu)$, with multipoles $\xi_0(s)$ (monopole) and $\xi_2(s)$ (quadrupole) evaluated via Legendre projection, and configuration-space bins covering $0.01 < r < 100\,h^{-1} \mathrm{Mpc}$ (or $2<r<150\,h^{-1}\mathrm{Mpc}$ in BOSS/eBOSS), as well as corresponding Fourier-space power spectra $P_\ell(k)$ extending up to $k=0.7\,h\,\mathrm{Mpc}^{-1}$ (pypower FFT estimator). Large-scale bias $b$ is fit by matching the measured monopole in $10 < s < 40\,h^{-1} \mathrm{Mpc}$ to theory: $$\xi_0(s) = b^2 \left[1 + \frac{2\beta}{3} + \frac{\beta^2}{5}\right]\,\xi_{\rm lin}(s)$$ with $\beta = f/b \simeq \Omega_m(z)^{0.55}/b$ and $b$ parameterized as a function of $M_r$ or $M_\star$ thresholds.

Results demonstrate $<5\%$ agreement between Uchuu mocks and DESI data for $1<r<20\,h^{-1}\mathrm{Mpc}$ (monopole), with robust recovery of clustering and bias dependencies on stellar mass, luminosity, and redshift. LRG quadrupole deviations at small scales ($\sim 5-15\%$) 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., $\xi_\ell$, $P_\ell$), the empirical covariance is: $$\mathrm{Cov}_{ij} = \langle [X_i - \langle X_i \rangle][X_j - \langle X_j \rangle] \rangle$$ with rescaling for effective survey volume $V_{\rm eff}$ 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 $10-60\%$ for $r < 20\,h^{-1}\,\mathrm{Mpc}$ (Ereza et al., 2023). This highlights the necessity of high-fidelity $N$-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 $V_{\rm peak}$ 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).