Ulagam Simulation Suite: Cosmological Insights

• Ulagam Simulation Suite is a comprehensive set of large-volume cosmological N-body simulations designed to probe diverse primordial non-Gaussian signatures.
• It implements an innovative non-Gaussian initial condition generation method using separable basis expansions to reduce computational complexity via FFTs.
• The suite produces detailed observables such as weak lensing maps, halo catalogs, and bispectra, enabling precise forecasts for upcoming lensing surveys.

The Ulagam Simulation Suite is a comprehensive, publicly released set of large-volume cosmological N-body simulations tailored to investigate the imprints of primordial non-Gaussianities (PNGs) on the cosmic large-scale structure (LSS) and late-time observables such as weak gravitational lensing. By enabling arbitrary primordial bispectrum templates—including complex “cosmological collider” signals with non-separable and scale-dependent features—the suite advances the field beyond the limitations of analytic and perturbative approaches, and provides a numerical laboratory for precision cosmology and testing of inflationary physics.

1. Architecture and Scope of the Ulagam Simulation Suite

The Ulagam Simulation Suite is built on the PKDGRAV3 N-body solver and is purpose-designed to model the nonlinear evolution of cosmic structure from primordial initial conditions with non-Gaussian signatures through to the present epoch (Anbajagane et al., 2023, Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025). The scope of Ulagam encompasses:

• Full-sky N-body simulations with millions of particles, evolving both standard Gaussian and non-Gaussian (PNG) initial conditions.
• Initial conditions that admit a diverse set of PNG templates, including local, equilateral, orthogonal, and many “cosmological collider” models motivated by particle physics in the early universe.
• Simulation outputs including three-dimensional density fields, two-dimensional projected density shells (lightcones), halo catalogs (using, e.g., Rockstar), and lensing convergence maps.

A core component is the capacity to evolve over thirty distinct bispectrum templates, comprising both separable and non-separable (oscillatory, scale-dependent, or angular-dependent) signatures, thus exceeding the typical scope of simulations designed for galaxy clustering or CMB analyses.

2. Methodology: Non-Gaussian Initial Condition Generation

A central innovation of the Ulagam Suite is an efficient methodology for injecting arbitrary PNG signals into the initial density field, leveraging a separable basis expansion for the primordial bispectrum:

• The initial gravitational potential $\phi_{\rm NG}(\mathbf{k})$ is constructed via

$$\phi_{\rm NG}(\mathbf{k}) = \phi_{\rm G}(\mathbf{k}) + \int d^3\mathbf{k}_1 d^3\mathbf{k}_2\, (2\pi)^3 \delta_D(\mathbf{k}-\mathbf{k}_1-\mathbf{k}_2) K_{12}(k_1, k_2, k_3) \phi_G(\mathbf{k}_1)\phi_G(\mathbf{k}_2)$$

where $K_{12}$ is the kernel encoding the bispectrum shape, and $\phi_{\rm G}$ is a Gaussian random field (Anbajagane et al., 2 Sep 2025).

• To make this computation tractable, $K_{12}$ (and thus the bispectrum $B(k_1,k_2,k_3)$) is expanded as

$$S(k_1,k_2,k_3) = \sum_{i,j,k} \alpha_{ijk} q_i(k_1)q_j(k_2)q_k(k_3)$$

where the $q_i$ are basis functions (e.g., modified Legendre polynomials) and $\alpha_{ijk}$ are coefficients determined by iterative solvers. This decomposition enables each term to be evaluated using Fast Fourier Transforms, reducing the computational scaling from $O(N^6)$ to $O(N^3\log N)$.

• The public initial condition generator, "Aarambam," implements this methodology and is accessible at https://github.com/DhayaaAnbajagane/Aarambam (Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025).

This approach allows the simulation of primordial features beyond the standard templates, incorporating scale-dependent oscillations, resonances, and general non-separability, as predicted by many inflationary models.

3. Simulated Observables and Summary Statistics

The analysis pipeline of the Ulagam Suite produces simulated observables relevant for direct comparison with data from current and upcoming surveys, notably LSST, Euclid, and Roman (Anbajagane et al., 2023, Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025). The key outputs and statistics include:

• Weak Lensing Convergence Maps: Three-dimensional N-body outputs are projected along the line-of-sight with appropriate lensing kernels to obtain full-sky maps of the lensing convergence field, $\kappa(\theta)$.
• Moments of the Convergence Field: The $N$th moment is defined as

$$\langle \kappa^N \rangle (\theta) = \frac{1}{N_{\rm pix}}\sum_{i=1}^{N_{\rm pix}} (\kappa_i(\theta))^N,$$

with smoothing scale $\theta$ induced by a filter, typically a tophat $W_{\ell}(\theta) = 2j_1(\ell\theta)/(\ell\theta)$.

• Cumulative Distribution Functions (CDFs): For a given smoothing scale, the fraction of sky with convergence above a threshold, encapsulating integrated information from all $N$-point functions.
• Full Three-Point Correlation Functions (Bispectra): These are measured from the convergence field to capture information on configuration/shape dependence of non-Gaussianity that is inaccessible to angle-averaged moments.
• Halo Catalogs and Mass Function: Halo finding (e.g., with Rockstar) produces catalogs enabling studies of halo abundance, bias, and their scale-dependent responses to PNGs.

These observables are used in concert to estimate the Fisher information matrix for PNG amplitude parameters (e.g., $f_{\rm NL}$ for local, equilateral, orthogonal, and other templates), breaking degeneracies with standard parameters $(\Omega_m, \sigma_8)$ and nuisance parameters (such as intrinsic alignments).

4. Constraining Power and Scientific Findings

The Ulagam Simulation Suite provides detailed forecasts for the sensitivity of weak gravitational lensing—particularly from the Rubin Observatory LSST—to primordial non-Gaussianity parameters (Anbajagane et al., 2023, Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025). Core findings include:

• For an LSST Year 10 dataset, forecasted 1σ constraints are:
  • $\sigma(f_{\rm NL}^{\rm eq}) \approx 110$
  • $\sigma(f_{\rm NL}^{\rm or,lss}) \approx 120$
  • $\sigma(f_{\rm NL}^{\rm loc}) \approx 40$ (Anbajagane et al., 2023)
• For equilateral and orthogonal-like PNGs, lensing constraints are comparable to, or better than, those expected from galaxy clustering (e.g., DESI), especially for templates not inducing strong scale-dependent galaxy bias.
• Lensing is particularly competitive for PNG signatures peaking at smaller scales ($k \gtrsim 0.2\,h/{\rm Mpc}$) and for complex features (oscillations, resonances, excited states) that cannot be effectively probed by the CMB (Anbajagane et al., 2 Sep 2025).
• Lensing captures information at non-linear scales and low redshift ($z\lesssim 1.25$), where gravitational collapse of massive halos modulates the primordial signatures. The constraining power is primarily sourced from these non-linear regimes (Anbajagane et al., 2023).
• Conservative scale cuts (excluding scales below $\sim 20$ arcmin) degrade constraints by $\sim60\%$, but remaining information still yields competitive PNG sensitivity—advantageous since small-scale systematics (e.g., baryonic effects) are less problematic (Anbajagane et al., 2023).
• For PNG types generating strong, distinctive scale-dependent galaxy bias ($k^{-2}$ scaling), galaxy clustering remains superior; however, lensing provides a probe free from uncertainties in galaxy–halo connection (Anbajagane et al., 2023).
• Joint analysis of higher order statistics (moments, CDFs, bispectra) offers substantial gains by breaking parameter degeneracies.

The simulations also highlight non-monotonic and scale-dependent phenomenology in the halo abundance and matter power spectrum for specific PNG templates, further enriching the scientific diagnostic set (Anbajagane et al., 2 Sep 2025).

5. Data Products, Accessibility, and Community Resources

The Ulagam Simulation Suite is accompanied by a robust set of public data products and software tools, supporting reproducibility and survey-oriented research (Anbajagane et al., 2023, Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025). The released resources include:

Simulation Output	Description	Access
3D Density Fields	Evolved matter field snapshots	Project repository
2D Density Shells (Lightcones)	Projected full- or partial-sky mass maps at varied $z$	Project repository
Halo Catalogs	Catalogs from halo-finder (e.g., Rockstar)	Project repository
Lensing Convergence Maps	Full-sky $\kappa(\theta)$ fields for lensing analyses	Project repository
Aarambam Initial Conditions Generator	Code for arbitrary bispectrum PNG injection	GitHub/Aarambam

Researchers are encouraged to use and extend these data and codes for new analyses, to test systematics, and to build customized survey pipelines. The data are documented in accompanying online resources (e.g., project websites, readthedocs).

6. Context and Implications for Cosmological Inference

The Ulagam Simulation Suite bridges the theoretical and observational frontier in precision cosmology by enabling end-to-end, simulation-based forecasts and systematic studies of PNG signatures in the nonlinear universe (Anbajagane et al., 2023, Anbajagane et al., 2 Sep 2025, Anbajagane et al., 2 Sep 2025). Notable implications include:

• The ability to simulate and forecast cosmological collider PNGs—arising from massive particle interactions during inflation—at nonlinear scales, incorporating complex signatures previously inaccessible in perturbative or analytic work.
• Improved modeling of systematic effects inherent in weak lensing and halo-based observables, by directly simulating the evolution of PNG features through cosmic time.
• A simulation-based foundation for multi-probe analyses, where weak lensing, halo abundance, and clustering can be combined to jointly constrain inflationary microphysics.
• Demonstration that lensing analyses are not only competitive with CMB and galaxy clustering for a broad class of models, but also, for sharply scale-dependent or oscillatory features, potentially deliver leading constraints.
• Open dissemination of simulations and pipeline tools enables survey collaborations and theorists to test, refine, and improve both large-scale structure inference and cosmic inflationary physics.

This suggests a trajectory toward simulation-based inference as a standard methodology in cosmology. A plausible implication is synergistic improvements in constraints through joint analysis of CMB, lensing, and galaxy surveys, and further exploration of richly-parameterized inflationary models using the Ulagam infrastructure.