SIDES-Uchuu Simulation Framework

• SIDES-Uchuu is a synthetic-survey framework based on ultra-large dark-matter simulations, enabling forward modeling of galaxy surveys and cosmological inference.
• It integrates multiple simulation runs—such as Uchuu, Shin-Uchuu, and GLAM-Uchuu—to deliver high resolution, large volumes, and comprehensive halo statistics across cosmic epochs.
• Its products, including realistic lightcones and calibrated halo models, support precise survey calibration, covariance estimation, and dynamic analyses in cosmology.

As used across the Uchuu literature, SIDES-Uchuu is best understood as the Uchuu-based synthetic-survey framework built on the ultra-large dark-matter-only cosmological $N$-body simulations of the Uchuu suite and on downstream products such as halo catalogs, merger trees, SHAM lightcones, and UniverseMachine galaxy catalogs. Its numerical foundation is the flagship Uchuu run, with $12800^3 \simeq 2.1\times10^{12}$ particles in a $2000\,h^{-1}\mathrm{Mpc}$ cube, complemented by higher-resolution and ensemble runs that extend the dynamic range from dwarf-galaxy hosts to rich clusters and from local-survey lightcones to high-redshift halo statistics (Ishiyama et al., 2020). In practice, SIDES-Uchuu-style products are used for forward modeling of galaxy surveys and for controlled validation of cosmological inference pipelines, including clustering, BAO/RSD, void statistics, halo mass functions, and peculiar-velocity measurements (Dong-Páez et al., 2022).

1. Simulation suite and numerical scope

The core Uchuu suite was introduced as a set of ultra-large, high-resolution cosmological $N$-body simulations designed to provide the volume and mass resolution required for modern survey mock catalogs and semi-analytic galaxy modeling. The flagship run, Uchuu, evolves $12800^3$ particles in a box of side length $2000\,h^{-1}\mathrm{Mpc}$, with particle mass $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$ and gravitational softening $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$. The highest-resolution run, Shin-Uchuu, uses $6400^3$ particles in a $140\,h^{-1}\mathrm{Mpc}$ box, reaching $12800^3 \simeq 2.1\times10^{12}$0 with $12800^3 \simeq 2.1\times10^{12}$1. Additional scaling runs include mini-Uchuu ($12800^3 \simeq 2.1\times10^{12}$2 in $12800^3 \simeq 2.1\times10^{12}$3) and micro-Uchuu ($12800^3 \simeq 2.1\times10^{12}$4 in $12800^3 \simeq 2.1\times10^{12}$5), which share the Uchuu mass resolution, and the very high-resolution auxiliary run Phi-4096 ($12800^3 \simeq 2.1\times10^{12}$6 in $12800^3 \simeq 2.1\times10^{12}$7, $12800^3 \simeq 2.1\times10^{12}$8), which extends concentration studies to very low-mass halos at $12800^3 \simeq 2.1\times10^{12}$9 (Ishiyama et al., 2020).

Run or ensemble	Numerical specification	Primary role
Uchuu	$2000\,h^{-1}\mathrm{Mpc}$0, $2000\,h^{-1}\mathrm{Mpc}$1, $2000\,h^{-1}\mathrm{Mpc}$2	Flagship large-volume backbone
Shin-Uchuu	$2000\,h^{-1}\mathrm{Mpc}$3, $2000\,h^{-1}\mathrm{Mpc}$4, $2000\,h^{-1}\mathrm{Mpc}$5	Highest-resolution main run
mini-/micro-Uchuu	$2000\,h^{-1}\mathrm{Mpc}$6 in $2000\,h^{-1}\mathrm{Mpc}$7; $2000\,h^{-1}\mathrm{Mpc}$8 in $2000\,h^{-1}\mathrm{Mpc}$9	Tests and smaller-volume applications
Phi-4096	$N$0, $N$1, $N$2	Very low-mass high-$N$3 halos
Mucho-Uchuu ensembles	50 realizations at $N$4, 300 at $N$5, 100 at $N$6	Variance-reduced HMF calibration
GLAM-Uchuu	$N$7, $N$8, $N$9	Large covariance ensembles

The suite is not limited to a single numerical product. In the halo-mass-function study, “Uchuu simulations” explicitly denotes six simulation types—Phi-4096, Shin-Uchuu, Uchuu, Mucho-Uchuu-140M, Mucho-Uchuu-1G, and Mucho-Uchuu-6G—with 452 realizations in total when ensemble members are counted. These runs use GreeM for the TreePM evolution, RockStar or MPI-Rockstar for halo identification, and Consistent Trees for merger trees (Fernández-García et al., 5 Dec 2025).

A notable technical point is that different parts of the Uchuu ecosystem are described with closely related, but not identical, cosmological parameter sets. The original DR1 description states that all runs adopt Planck 2020 cosmological parameters and start from $12800^3$0, providing 50 snapshots covering $12800^3$1 (Ishiyama et al., 2020). By contrast, several downstream applications describe Uchuu as a Planck 2015 simulation, while the Mucho-Uchuu ensembles are quoted as Planck 2018 in the HMF study (Fernández-García et al., 5 Dec 2025). This suggests that precise interpretation of any SIDES-Uchuu product requires attention to the exact run, realization family, and cosmological convention being used.

2. Released dark-matter products and halo statistics

The first Uchuu data release was organized around the dark-matter products most immediately useful for forward modeling. Uchuu Data Release 1 (DR1) includes subsets of particles, dark-matter power spectra, halo and subhalo catalogs, and halo/subhalo merger trees; data are distributed publicly via the Skies & Universes site, with particle data in Gadget-2 format and some products in HDF5. Future releases were stated to include gravitational lensing maps and mock galaxy, X-ray cluster, and AGN catalogs (Ishiyama et al., 2020).

A central DR1 result is the nonlinear matter power spectrum over an unusually wide dynamic range. Uchuu and Shin-Uchuu agree in their overlap region, $12800^3$2, and the combined spectra span roughly five decades in wavenumber. The simulation analysis concludes that the calculations remain reliable from the BAO scale down to very small scales. Comparisons against standard nonlinear fitting formulas show that the Smith et al. model matches Uchuu to $12800^3$3 at $12800^3$4 and $12800^3$5 up to $12800^3$6, while the Takahashi et al. and Mead et al. models are typically accurate to $12800^3$7 over the tested ranges (Ishiyama et al., 2020).

The halo and subhalo catalogs provide comparable leverage. The distinct halo mass function is measured down to halos with more than 40 particles, corresponding to $12800^3$8 in Uchuu and $12800^3$9 in Shin-Uchuu, yielding a combined mass range of nearly eight decades. Comparison with the Despali et al. fitting function shows agreement at the $2000\,h^{-1}\mathrm{Mpc}$0 level over broad mass ranges, with differences rising to $2000\,h^{-1}\mathrm{Mpc}$1 at high redshift and at the most massive end. The subhalo mass function $2000\,h^{-1}\mathrm{Mpc}$2 has a low-mass slope close to $2000\,h^{-1}\mathrm{Mpc}$3 and a clearer exponential tail than earlier work. This is particularly relevant for SIDES-Uchuu-style applications that require realistic substructure populations and host-mass dependence (Ishiyama et al., 2020).

Another practically important output is the recalibrated halo concentration model, based on the functional form of Diemer & Joyce (2019) but refit to Uchuu:

$2000\,h^{-1}\mathrm{Mpc}$4

For all halos with the $2000\,h^{-1}\mathrm{Mpc}$5 method and $2000\,h^{-1}\mathrm{Mpc}$6, the best-fit parameters are $2000\,h^{-1}\mathrm{Mpc}$7, $2000\,h^{-1}\mathrm{Mpc}$8, $2000\,h^{-1}\mathrm{Mpc}$9, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$0, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$1, and $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$2; for the profile-fit version of $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$3, they are $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$4, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$5, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$6, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$7, $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$8, and $m_{\rm p}=3.27\times10^{8}\,h^{-1}M_\odot$9. Equivalent parameter sets are provided for $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$0, $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$1, and for relaxed halos. Residuals are typically within $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$2 over nearly eight orders of magnitude in halo mass and across $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$3, with some cases reaching $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$4. The reported upturn in the mass-concentration relation occurs for all halos and for relaxed halos at $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$5, whereas no upturn is detected at $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$6 (Ishiyama et al., 2020).

3. Galaxy assignment and survey-realistic lightcones

The survey-facing side of SIDES-Uchuu is built by adding galaxies to the dark-matter backbone and projecting the result into realistic lightcones. In the SDSS implementation, the galaxy population is assigned by subhalo abundance matching with $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$7 as the ranking variable, where $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$8 is the maximum of $\varepsilon=4.27\,h^{-1}\mathrm{kpc}$9 over the halo’s history. The target luminosity function is interpolated between SDSS and GAMA,

$6400^3$0

with

$6400^3$1

and a Gaussian scatter of fixed width $6400^3$2 is added to the luminosity proxy before re-ranking. Six snapshots at $6400^3$3 are stitched into spherical shells around an observer, redshift includes line-of-sight peculiar velocities, and the full-sky catalog is cut to the SDSS northern contiguous footprint with a HEALPix mask. This process yields 32 lightcones, of which 8 are fully independent below $6400^3$4, while the full set is independent below $6400^3$5 (Dong-Páez et al., 2022).

These Uchuu-SDSS lightcones carry galaxy positions, redshifts, apparent and absolute $6400^3$6 magnitudes, rest-frame $6400^3$7 colours, stellar masses, star formation rates, and detailed halo properties. Fibre collisions are modeled explicitly with a friends-of-friends grouping in angular space at the SDSS $6400^3$8 collision radius, followed by nearest-neighbour redshift assignment and restoration of about $6400^3$9 of collided galaxies to mimic plate overlaps. The resulting fiber-collision fraction is close to SDSS, with $140\,h^{-1}\mathrm{Mpc}$0 in the mocks versus $140\,h^{-1}\mathrm{Mpc}$1 in the data. The released products include 32 Uchuu-SDSS lightcones, six box catalogues, 5100 Uchuu/GLAM SDSSbao lightcones, a companion SDSS large-scale-structure catalogue, and random catalogues for clustering analyses (Dong-Páez et al., 2022).

The same high-resolution backbone has been repurposed for other survey families. For BOSS and eBOSS LRGs, Uchuu lightcones are built with SHAM on resolved halos and subhalos, while 16,000 GLAM-Uchuu lightcones supply covariance estimates. The mock construction explicitly matches angular mask, redshift distribution $140\,h^{-1}\mathrm{Mpc}$2, completeness, and fiber collisions, and the resulting catalogs reproduce correlation functions and power spectra across $140\,h^{-1}\mathrm{Mpc}$3. A central methodological result is that approximate mock covariances such as MD-Patchy and EZmock can underestimate errors by roughly $140\,h^{-1}\mathrm{Mpc}$4, depending on statistic and scale (Ereza et al., 2023).

For DESI DR2, the Uchuu-BGS and Uchuu-LRG reference mocks extend the same logic to BGS-BRIGHT and LRG selections. Both use $140\,h^{-1}\mathrm{Mpc}$5-based SHAM, assign baryonic properties tracer by tracer, and generate survey-like lightcones in spherical shells of width $140\,h^{-1}\mathrm{Mpc}$6 cut to the DESI footprints. The reported clustering agreement is better than $140\,h^{-1}\mathrm{Mpc}$7 for separations $140\,h^{-1}\mathrm{Mpc}$8 and below $140\,h^{-1}\mathrm{Mpc}$9 for $12800^3 \simeq 2.1\times10^{12}$00, with consistency in the large-scale bias trends as functions of luminosity for BGS-BRIGHT and stellar mass for LRGs (Fernández-García et al., 2 Jul 2025).

4. Cosmological inference pipelines calibrated on Uchuu

One major use of SIDES-Uchuu products is the end-to-end validation of cosmological inference pipelines under controlled conditions. In the void-statistics analysis of SDSS DR7, the Uchuu simulation serves simultaneously as calibration set, validation set, and source of realistic lightcones. Voids are defined as maximal non-overlapping empty spheres around tracer points. Candidate voids are generated from Delaunay circumspheres and then filtered so that the final catalog contains only disjoint maximal spheres. Two summary statistics are used: the Void Probability Function $12800^3 \simeq 2.1\times10^{12}$01 and the abundance of voids larger than $12800^3 \simeq 2.1\times10^{12}$02, denoted $12800^3 \simeq 2.1\times10^{12}$03 or $12800^3 \simeq 2.1\times10^{12}$04. The theoretical framework adopts

$12800^3 \simeq 2.1\times10^{12}$05

with calibrated coefficients $12800^3 \simeq 2.1\times10^{12}$06 and $12800^3 \simeq 2.1\times10^{12}$07, together with a saturation prescription $12800^3 \simeq 2.1\times10^{12}$08 for sufficiently large $12800^3 \simeq 2.1\times10^{12}$09. The SDSS sample is defined by $12800^3 \simeq 2.1\times10^{12}$10 and $12800^3 \simeq 2.1\times10^{12}$11, yielding $12800^3 \simeq 2.1\times10^{12}$12, 112,496 galaxies, and $12800^3 \simeq 2.1\times10^{12}$13. Void-only constraints are broad, but the contours are nearly orthogonal to weak-lensing contours in the $12800^3 \simeq 2.1\times10^{12}$14-$12800^3 \simeq 2.1\times10^{12}$15 plane; combining SDSS voids with KiDS-1000 and DESY3 yields $12800^3 \simeq 2.1\times10^{12}$16, $12800^3 \simeq 2.1\times10^{12}$17, $12800^3 \simeq 2.1\times10^{12}$18, and $12800^3 \simeq 2.1\times10^{12}$19 (Fernández-García et al., 2024).

A second example is the low-redshift SN Ia peculiar-velocity validation for TITAN. Here Uchuu provides the “ground truth” large-scale structure on which both the galaxy density reconstruction and the SN realizations are based. The analysis uses the associated UniverseMachine galaxy catalog, extracts eight independent $12800^3 \simeq 2.1\times10^{12}$20 subvolumes, generates roughly 2000 simulated SNe Ia at $12800^3 \simeq 2.1\times10^{12}$21 with SNANA inside the Pippin pipeline, and reconstructs density fields intended to emulate the 2M++ workflow. The growth-rate fit uses a modified forward likelihood with

$12800^3 \simeq 2.1\times10^{12}$22

and an effective covariance

$12800^3 \simeq 2.1\times10^{12}$23

Across eight realizations, the recovered mean is $12800^3 \simeq 2.1\times10^{12}$24, with $12800^3 \simeq 2.1\times10^{12}$25 and $12800^3 \simeq 2.1\times10^{12}$26, compared with the Uchuu input $12800^3 \simeq 2.1\times10^{12}$27. The mock-to-mock scatter is $12800^3 \simeq 2.1\times10^{12}$28, and the dominant single systematic is the intrinsic scatter model for the SNe; C11 produces $12800^3 \simeq 2.1\times10^{12}$29, G10 gives $12800^3 \simeq 2.1\times10^{12}$30, and cutting red SNe at $12800^3 \simeq 2.1\times10^{12}$31 reduces the C11 bias (Dixon et al., 12 Jun 2026).

These applications show that Uchuu is not used merely as a source of catalog realizations. It functions as a numerical laboratory in which the mapping from dark matter to survey observables, covariance propagation, and parameter recovery can be tested against a known cosmological input.

5. Theoretical and dynamical extensions

The Uchuu suite has also been used as a precision benchmark for new theoretical descriptions of halo statistics. In the GPS+ halo-mass-function framework, the HMF is written as

$12800^3 \simeq 2.1\times10^{12}$32

with a collapsed mass fraction

$12800^3 \simeq 2.1\times10^{12}$33

The fit is performed over bins with relative uncertainty below $12800^3 \simeq 2.1\times10^{12}$34, yielding $12800^3 \simeq 2.1\times10^{12}$35, $12800^3 \simeq 2.1\times10^{12}$36, and $12800^3 \simeq 2.1\times10^{12}$37. Using six simulation types and 452 total realizations, the calibrated HMF spans $12800^3 \simeq 2.1\times10^{12}$38 over $12800^3 \simeq 2.1\times10^{12}$39, with a completeness cut of at least 407 particles per halo. GPS+ reproduces the simulated HMF typically to within $12800^3 \simeq 2.1\times10^{12}$40, while Sheth-Tormen performs similarly only at $12800^3 \simeq 2.1\times10^{12}$41 and can deviate by $12800^3 \simeq 2.1\times10^{12}$42 near $12800^3 \simeq 2.1\times10^{12}$43. The same study finds that $12800^3 \simeq 2.1\times10^{12}$44 yields a more universal, nearly redshift-independent HMF than $12800^3 \simeq 2.1\times10^{12}$45, and that the virial definition can induce discrepancies of about $12800^3 \simeq 2.1\times10^{12}$46 at the high-mass end at $12800^3 \simeq 2.1\times10^{12}$47 (Fernández-García et al., 5 Dec 2025).

On the dynamical side, the Uchuu-UniverseMachine mock galaxy catalog has been used to measure the velocity anisotropy profile of galaxy clusters. The cluster sample is defined by $12800^3 \simeq 2.1\times10^{12}$48 and extends to $12800^3 \simeq 2.1\times10^{12}$49; the sample contains $12800^3 \simeq 2.1\times10^{12}$50 clusters at $12800^3 \simeq 2.1\times10^{12}$51, 139,165 at $12800^3 \simeq 2.1\times10^{12}$52, 37,443 at $12800^3 \simeq 2.1\times10^{12}$53, and 7,284 at $12800^3 \simeq 2.1\times10^{12}$54. The central diagnostic is

$12800^3 \simeq 2.1\times10^{12}$55

for which the profile rises from $12800^3 \simeq 2.1\times10^{12}$56 near the center to a peak of about $12800^3 \simeq 2.1\times10^{12}$57 at $12800^3 \simeq 2.1\times10^{12}$58, dips near $12800^3 \simeq 2.1\times10^{12}$59, and rises again in the outskirts. More massive clusters have larger $12800^3 \simeq 2.1\times10^{12}$60 at essentially all radii, with representative $12800^3 \simeq 2.1\times10^{12}$61 for low-mass systems and $12800^3 \simeq 2.1\times10^{12}$62 for the most massive clusters. Redshift evolution is also strong: at $12800^3 \simeq 2.1\times10^{12}$63, $12800^3 \simeq 2.1\times10^{12}$64 at $12800^3 \simeq 2.1\times10^{12}$65, while at $12800^3 \simeq 2.1\times10^{12}$66 it is $12800^3 \simeq 2.1\times10^{12}$67 at $12800^3 \simeq 2.1\times10^{12}$68. The same analysis provides redshift-dependent power-law relations of the form $12800^3 \simeq 2.1\times10^{12}$69 for the hydrostatic, infall, and turnaround radii (Abdullah et al., 6 Apr 2025).

Taken together, these extensions place SIDES-Uchuu beyond survey mocking in the narrow sense. The framework also supports theoretical recalibration of halo abundance models and dynamical interpretation of the phase-space structure of clusters.

6. Methodological significance, limitations, and interpretation

A consistent feature of SIDES-Uchuu work is the separation between high-fidelity matter realization and large-ensemble covariance generation. Uchuu itself provides the subhalo-resolved backbone needed for SHAM and for accurate small-scale clustering, whereas GLAM-Uchuu supplies the thousands of realizations needed for covariance estimation. This division of labor is explicit in the BOSS/eBOSS analysis, where Uchuu plus SHAM is used for physically faithful lightcones and GLAM plus HOD for large covariance ensembles (Ereza et al., 2023).

Several limitations are equally explicit in the literature. In the SDSS lightcones, colour-dependent clustering is less precise than luminosity- or stellar-mass-dependent clustering because colours are drawn statistically from an empirical distribution rather than being tied to halo assembly history. The brightest luminosity and highest-mass samples indicate that the true scatter in the galaxy–halo connection probably decreases at the high-luminosity end (Dong-Páez et al., 2022). In the DESI LRG reference mocks, the main residual tension appears in the quadrupole at $12800^3 \simeq 2.1\times10^{12}$70, which is attributed to imperfect velocity modeling in SHAM and the use of broad redshift bins (Fernández-García et al., 2 Jul 2025).

The literature also identifies concrete sources of systematic uncertainty that are easy to overlook if SIDES-Uchuu products are treated as generic “mocks.” Approximate covariance schemes can understate errors by $12800^3 \simeq 2.1\times10^{12}$71 relative to $12800^3 \simeq 2.1\times10^{12}$72-body-based GLAM-Uchuu estimates (Ereza et al., 2023). Halo mass-definition choices matter: $12800^3 \simeq 2.1\times10^{12}$73 behaves more nearly universally than $12800^3 \simeq 2.1\times10^{12}$74 in the GPS+ HMF study (Fernández-García et al., 5 Dec 2025). In SN Ia peculiar-velocity work, the intrinsic scatter model dominates the single-survey systematic budget, and red SNe with skewed colour distributions can mimic part of the velocity signal (Dixon et al., 12 Jun 2026).

A final source of potential confusion is nomenclature. “Uchuu” may refer to the single $12800^3 \simeq 2.1\times10^{12}$75 flagship box, to the broader multi-resolution Uchuu suite, or to downstream galaxy-populated products such as Uchuu-SDSS, Uchuu-BGS, Uchuu-LRG, or Uchuu-UniverseMachine. This suggests that SIDES-Uchuu is less a single simulation than a layered framework: a dark-matter numerical backbone, a set of halo and merger-tree products, and multiple survey-specific forward models built for direct comparison with observational pipelines.

Within that layered framework, the principal significance of SIDES-Uchuu lies in the coexistence of very large cosmological volume, high enough mass resolution to retain substructure, public dark-matter products, and survey-realistic lightcone construction. That combination has made the Uchuu ecosystem a benchmark platform for mock catalog generation, covariance estimation, theoretical calibration, and end-to-end validation of low-redshift large-scale-structure observables.