Manticore-Local: Bayesian Simulations of Local Cosmos

• Manticore-Local is a suite of Bayesian-constrained simulations that reconstructs the three-dimensional matter density of the local Universe using galaxy surveys and the BORG algorithm.
• It employs high-dimensional Hamiltonian Monte Carlo sampling and nonlinear gravitational solvers to evolve initial conditions into realistic cosmic structures.
• The method enables robust identification of clusters and voids, precise peculiar velocity reconstruction, and improved cosmological parameter estimation through rigorous uncertainty quantification.

Manticore-Local is a suite of Bayesian constrained simulations of the local Universe designed to provide physically consistent realizations of cosmic structure by fitting a structure formation model directly to observational galaxy data. Built upon the BORG (Bayesian Origin Reconstruction from Galaxies) algorithm and validated through extensive posterior predictive testing, Manticore-Local occupies a central methodological role in modern precision cosmology, enabling rigorous uncertainty quantification and robust analysis of environmental structure in the nearby cosmos.

1. Bayesian Constrained Inference of Local Cosmic Structure

Manticore-Local operates within a field-level Bayesian statistical framework that reconstructs the three-dimensional matter density field, δ(x), from galaxy position and redshift surveys (specifically, the 2M++ catalog). The relevant posterior is

$$P(\delta_{0} | d) \propto L(d | \delta_{0})\, \pi(\delta_{0})$$

where δ₀ is the initial density field, d represents the observed data, L is the likelihood obtained by forward modeling (i.e., predicting galaxy observables from δ₀ via structure formation simulations and a galaxy bias prescription), and π(δ₀) denotes the prior (homogeneous Gaussian random field matching early-Universe cosmology). The inference is conducted at the field level, producing a full multivariate posterior over initial density fluctuations rather than a simple point estimate, and thus encodes uncertainty and cosmic variance naturally.

2. BORG Algorithm and Nonlinear Evolution

The BORG algorithm underpins the Manticore-Local inference, employing a physical, Lagrangian approximation to structure formation (including second-order Lagrangian perturbation theory and N-body dynamics) to propagate the initial conditions forward in time, thereby generating synthetic realizations of the galaxy distribution. Hamiltonian Monte Carlo sampling traverses the extremely high-dimensional posterior (O(10⁸) dimensions), jointly fitting for initial conditions and nuisance parameters (e.g., non-linear, scale-dependent galaxy bias model). Each posterior sample is evolved with a nonlinear gravitational solver, producing constrained realizations statistically consistent with LCDM cosmology.

3. Posterior Predictive Consistency and Local Universe Realism

Validation of the Manticore-Local ensemble is performed using posterior predictive tests:

• The power spectra (P(k)) and bispectra of the simulated fields match those from both the observed 2M++ data and theoretical LCDM predictions.
• The initial condition samples demonstrate Gaussianity, consistent with expectations from the standard model of cosmological inflation.
• The halo mass function and spatial correlation statistics, as derived from the evolved simulations, adhere closely to analytic and simulation-based expectations.

These results confirm the statistical consistency of local cosmic structure with cosmological baseline models and verify that Manticore-Local does not find evidence for anomalous features such as a substantial local underdensity.

4. Precision Cluster and Void Identification

Manticore-Local’s posterior ensemble enables statistically robust identification of cosmic structures:

• Galaxy Clusters: Fourteen prominent clusters (Virgo, Coma, Perseus, etc.) are located in the simulation within one degree of their observed sky position, with 2–4σ detection significance across realizations. Counterparts’ reconstructed masses and redshifts agree with observational estimates, using probabilistic halo-matching schemes to enforce one-to-one associations.
• Voids: Using 50 posterior realizations, cosmic voids are extracted with the VIDE void finder (watershed applied to Voronoi tessellations of tracers). Properties (center, radius, shape) are described as posterior probability distributions, and a 5σ criterion is imposed using Poisson probability modeling to reject spurious detections, resulting in a catalog of 100 high-significance voids. Key formulas include the effective void radius:

$$R_\mathrm{eff} = \left( \frac{3V}{4\pi} \right)^{1/3}$$

and the center,

$$\vec{x}_\mathrm{center} = \frac{\sum_i V_i \vec{x}_i}{\sum_i V_i}$$

These catalogs serve as templates for environmental studies of galaxy evolution, lensing, and ISW analyses.

5. Peculiar Velocity Field Reconstruction and Cosmological Inference

By forward-evolving the inferred initial density and velocity fields, Manticore-Local reconstructs the peculiar velocity field of the local Universe. Comparisons with various independent datasets (including the SH0ES Cepheid distance ladder and velocity measurements) show that the Bayesian evidence for Manticore-Local’s velocity field surpasses that of alternative methods (e.g., linear theory, Wiener filtering, machine learning-based regressions), owing to its physically consistent, non-linear treatment. This capability allows for:

• Precise correction of local peculiar velocities in cosmological distance ladder analyses.
• Marginalization over cosmic variance, via repeated sampling over the posterior ensemble.
• Quantitative uncertainty propagation to derived cosmological parameters.

A notable application is the recent 1.8% precision measurement of the Hubble constant ($$H_0 = 71.7 \pm 1.3~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$$) using Cepheids alone, which leverages ensemble-averaged LOS velocities from Manticore-Local’s realizations. The full Bayesian model for this application includes hierarchical modeling of Cepheid observables, redshifts (incorporating peculiar velocities and inhomogeneous Malmquist bias), and joint inference of the density-weighted distance prior: $$\pi(r | \mathbf{\theta}) = \frac{r^2 b(r, \mathbf{\theta})}{\int_0^{R} {r'}^2 b(r', \mathbf{\theta})\,dr'}$$ with a galaxy-bias factor $b(r,\mathbf{\theta})$ parametrized as a double power law of the local density.

6. Uncertainty Quantification and Ensemble Statistics

A defining feature of Manticore-Local is its delivery of a full field-level Bayesian posterior, enabling rigorous uncertainty quantification. For any derived field or observable—matter density, halo mass, velocities, void properties—the spread of realizations provides a direct measure of statistical and systematic uncertainties (arising from measurement error, observational masks, galaxy selection, cosmic variance, bias modeling, etc.). The formalism for the posterior on any observable O is: $$P(O | d) = \int \delta[O - O(\delta_0)]\, P(\delta_0 | d) \, d\delta_0$$ This rigorous propagation of uncertainty is critical for robust cosmological inference and for applications that require probabilistic structure templates.

7. Applications and Future Prospects

The Manticore-Local suite advances the state-of-the-art in constrained local Universe simulations, providing a robust digital twin for:

• Galaxy evolution and environmental physics studies, permitting selection and cross-matching of galaxies, clusters, and voids under realistic density and velocity field conditions.
• Cross-correlation studies involving lensing, ISW, and large-scale flows.
• Systematic error analysis for cosmological distance ladders and local parameter estimation, especially in quantifying and controlling inhomogeneous Malmquist bias and velocity-induced redshift errors.
• Development of methodologies extendable to larger supervolumes or with inclusion of additional hydrodynamical and astrophysical physics (e.g., in future Manticore-Deep projects).

The ensemble approach, probabilistic cluster/void catalogs, and improved handling of systematics position Manticore-Local as an essential tool for future observational and theoretical studies of the cosmic web, providing both a sophisticated statistical underpinning and high-fidelity physical reconstructions of the local cosmic environment.