CosmoGridV1 Suite: N-body Lightcone Simulations

• CosmoGridV1 Suite is a comprehensive set of N-body lightcone simulations that provide a dense grid of wCDM cosmologies for detailed map-level inference.
• It employs GPU-accelerated PkdGrav3 simulations and a modular post-processing pipeline to produce full-sky HEALPix maps for observables like weak lensing and galaxy clustering.
• The suite features rigorous benchmark validations and flexible baryon feedback modeling, supporting non-Gaussian statistics and machine-learning applications in cosmology.

CosmoGridV1 (CGV1) is a suite of large-scale $N$-body lightcone simulations designed to enable map-level cosmological inference with probes of large-scale structure. Developed explicitly to support non-Gaussian summary statistics, machine-learning applications, and Stage-III photometric survey forecasts, CosmoGridV1 provides a dense grid of $w$CDM cosmologies, each realized through multiple independent lightcone simulations. The dataset captures variations in key cosmological parameters while supplying a highly modular post-processing pipeline for forward-modeling a variety of observables, such as weak gravitational lensing, intrinsic alignment, and galaxy clustering, using consistent map-making recipes. CosmoGridV1 delivers raw and processed data products, benchmark validations, and open-source projection pipelines, and emphasizes reproducibility and flexibility for the community through its public data release.

1. Cosmological Parameter Coverage

CosmoGridV1 encompasses a six-dimensional parameter space within the $w$CDM framework, incorporating the sum of neutrino masses as a fixed background:

Parameter	Description	Variation
$\Omega_{\mathrm{m}}$	Present-day total matter density	Sobol grid
$\sigma_8$	RMS linear fluctuation amplitude (8 Mpc/h scale)	Sobol grid
$w_0$	Constant dark-energy equation-of-state	Sobol grid
$H_0$	Hubble parameter today	Sobol grid
$n_s$	Primordial power spectrum spectral index	Sobol grid
$\Omega_b$	Present-day baryon density	Sobol grid
$\sum m_\nu$	Total neutrino mass ($3$ degenerate species)	Fixed: $0.06$ eV

Parameter coverage is achieved via a 6D Sobol low-discrepancy sequence, split evenly between a "wide" prior box (appropriate for Stage-III survey analyses) and a "narrow" box informed by CMB constraints. A total of $2500$ discrete grid points are sampled, after imposing additional exclusion cuts to avoid physically inconsistent or observationally excluded regimes (e.g., phantom crossing with $w_0 < -1.1$ in the $N$-body gauge).

For each grid point, $7$ independent simulation seeds are generated—balancing the need to control map-level sample variance in non-Gaussian and ML summary statistics with computational efficiency. At the fiducial cosmology ($\Omega_{\mathrm{m}}=0.26$, $\sigma_8=0.84$, $w_0=-1$, $n_s=0.9649$, $\Omega_b=0.0493$, $H_0=67.3$), $200$ independent realizations are provided, together with $\pm\Delta$ finite-difference "stencil" perturbations along each parameter axis ($6 \times 2$ per seed, yielding $2600$ fiducial-point simulations).

This dense coverage supports sophisticated emulator training and likelihood-free inference by ensuring both broad and focused parameter exploration, while the multi-seed approach minimizes interpolation noise and sample variance in derived map statistics.

2. Simulation Framework and Technical Choices

All simulations are executed using the PkdGrav3 $N$-body code with GPU acceleration on the CSCS Piz Daint infrastructure. The principal simulation specifications are:

• Main grid and fiducial simulations: $L=900\,\mathrm{Mpc}/h$ box, $N_p=832^3$ dark-matter particles
• Fiducial particle mass: $9.1 \times 10^{10}\,h^{-1}M_\odot$ (varies across grid: $3.5$–$17.5 \times 10^{10}\,h^{-1}M_\odot$)
• Gravitational softening: $0.02 \times$ mean interparticle spacing
• Time integration: $140$ global timesteps (split as $70$ from $z=99 \rightarrow 4$ and $70$ from $z=4 \rightarrow 0$)
• Benchmarks:
  • "Big-box" mode ($L=2250\,\mathrm{Mpc}/h$, $N_p=2048^3$)
  • "High-res shells" mode ($500$ timesteps at $L=900\,\mathrm{Mpc}/h$, $N_p=832^3$)
  • "High-res particles" mode ($L=900\,\mathrm{Mpc}/h$, $N_p=2048^3$, $140$ timesteps)

For each simulation, on-the-fly lightcone outputs are stored as concentric shells, and Friends-of-Friends (FoF) halo catalog snapshots are generated for subsequent structural analyses and baryonification. The use of multiple simulation resolutions and box volumes, encompassed within the benchmark suite, is designed to validate the stability of non-Gaussian features and power spectra to choices of box size, particle density, and shell thickness.

3. Lightcone Outputs and Map Construction

Each lightcone simulation outputs $69$ radial shells extending to $z=3.5$, stored in HEALPix format at $n_{\mathrm{side}}=2048$. Shell boundaries correspond to discrete simulation timesteps, yielding mean comoving shell widths of $\langle \Delta r \rangle \sim 40\,\mathrm{Mpc}/h$ at $z\sim0$ and $\sim90\,\mathrm{Mpc}/h$ at $z\sim1.5$.

Observables are constructed in the Born approximation using the UFalcon map-making pipeline. The fundamental map type in a tomographic bin is formed by summing appropriately weighted shell masses:

$$m_{2\mathrm{D}}(\text{pix}) \simeq \sum_{b} W^m \int_{\Delta z_b} \frac{dz}{E(z)} \delta_{3\mathrm{D}}[\chi(z) \hat n^{\text{pix}}, z]$$

For lensing convergence, the continuous kernel is

$$\kappa(\hat n) = \int_{0}^{\chi_H} d\chi\,W(\chi)\,\delta(\chi\hat n)$$

with:

$$\begin{aligned} W^{WL}(z) &= \frac{3}{2}\Omega_m \int_z^{z_s} dz' \, n(z')\frac{\chi(z)\chi(z,z')}{\chi(z')} a(z)^{-1} \left/ \int n \right. \ W^{IA}(z) &= \int dz\,F(z)n(z) / \int n \ W^{G}(z) &= \int dz\,n(z) / \int n \end{aligned}$$

where $F(z)= -C_1\rho_{\mathrm{crit}}\Omega_m D_+(z)$, $$C_1 = 5\times 10^{-14} h^{-2} M_\odot\,\mathrm{Mpc}^3$$, and $D_+$ the linear growth factor.

This kernel approach enables forward-modeling of multiple observables, including weak lensing, intrinsic alignment (IA), and galaxy clustering, as full-sky or masked HEALPix maps for arbitrary tomographic redshift distributions $n(z)$.

4. Benchmark Simulations and Validation

Twenty-eight high-resolution benchmark simulations are carried out at the fiducial cosmological parameters, subdivided into three categories:

1. "Big-box" ($L=2250\,\mathrm{Mpc}/h$, $N_p=2048^3$)
2. "High-res particles" ($L=900\,\mathrm{Mpc}/h$, $N_p=2048^3$)
3. "High-res shells" ($L=900\,\mathrm{Mpc}/h$, $N_p=832^3$, $500$ timesteps)

All benchmark runs utilize the same shell-based lightcone procedure and HEALPix map-making pipeline as the main grid. Their purpose is to quantify the response of map features (means, covariances) to simulation box size, mass resolution, and shell thickness—critical for robustly validating that map-level statistics (such as peaks, Minkowski functionals, and power spectra) are insensitive to these simulation choices. This ensures that downstream analyses using CosmoGridV1 can rely on the statistical soundness of the predictions across differing target observables and inference strategies.

5. Baryon Feedback Modeling

To account for the effects of baryonic physics on the matter distribution, CosmoGridV1 implements a shell-based baryonification scheme following Schneider et al. (2019), applied in post-processing to each HEALPix shell. Halos are identified in situ in the $N$-body outputs (minimum 150 particles, corresponding to $M_{\mathrm{vir}}\gtrsim$few $10^{12}M_\odot$) and fitted with NFW density profiles for parameters $M, c$.

The projected mass profile for component $\chi$ is defined as:

$$M_\chi^p(r) = 2\pi \int_0^r s\,ds \int_{-z_{\mathrm{max}}}^{z_{\mathrm{max}}} dz\,\rho_\chi(s, z)$$

The baryonification-induced radial displacement $d^p(r|M,c)$ is then taken as the difference between baryonified and collisionless projected radii:

$$d^{p}(r|M, c) = r_{\mathrm{dmb}} [M_\chi^p] - r_{\mathrm{dmo}} [M_\chi^p]$$

Each shell is locally remapped using gnomonic-patch interpolation, such that pixels within the angular radius of each halo are displaced according to $d^p$. Both pre- and post-baryonified shells are made available, allowing users to reapply baryonification in post-processing with arbitrary baryon model parameters $(M_c^0, \nu)$. This approach enables systematic exploration of feedback uncertainties in observables derived from the CosmoGridV1 suite.

6. Map-Making Pipeline and Modular Post-Processing

The UFalcon code constitutes the map-making backbone for CosmoGridV1, operating as follows:

• Inputs: particle-count shells ($n_{\mathrm{side}}=2048$), user-specified $n(z)$, baryonification parameters, intrinsic-alignment (IA) bias, galaxy bias.
• Executes the Born approximation projection (as detailed in section 3), aggregating relevant kernel weights per observable.
• Intrinsic alignments are modeled through the nonlinear alignment (NLA) prescription, with $\kappa^{\mathrm{IA}}$ maps constructed using the $W^{\mathrm{IA}}(z)$ kernel.
• Galaxy clustering maps are constructed by biasing the matter density maps (linear or nonlinear bias, $b$), with shot noise incorporated as Poisson fluctuations.
• Outputs comprise full-sky HEALPix maps at $n_{\mathrm{side}}=2048$ (raw) and $512$ (forecast products), suitable for direct use in likelihood analyses, machine-learning pipelines, or summary statistics extraction.

This modularity confers flexibility: users can create custom maps for arbitrary galaxy selection functions $n(z)$, survey binning, and feedback model choices, all without rerunning the base $N$-body simulations.

7. Data Products, Distribution, and Usage

CosmoGridV1 offers the following publicly available data products:

• Raw particle-count shells for all 20,128 simulations ($n_{\mathrm{side}}=2048$, $69$ shells per simulation)
• Projected full-sky maps for a representative Stage-III survey forecast (lensing $\kappa$, IA, and $\delta_g$ in four tomographic bins, $n_{\mathrm{side}}=512$, no mask)
• Maps used in the KiDS-1000 deep-learning cosmology constraints, including extended sampling of baryonic feedback parameters
• Corresponding products for all $28$ high-resolution benchmark simulations

Users can regenerate custom maps by downloading raw shells, specifying arbitrary $n(z)$, and running the UFalcon pipeline (optionally including baryonification, IA, and bias). All data are distributed via Globus at www.cosmogrid.ai, with no proprietary restrictions.

CosmoGridV1 is expressly constructed for simulation-based inference at the map level, supporting both non-Gaussian statistics and machine-learning applications on current and forthcoming photometric survey data. Its open architecture and rigorous validation protocol enable end users to construct tailored observables, propagate baryonic and cosmological modeling uncertainties, and utilize both conventional and ML-based summary statistics in cosmological parameter estimation.