Manticore-Deep: Bayesian Digital Twins of Cosmic Structure Across SDSS and BOSS Volumes

Bayesian Digital Twins of Cosmic volume

The large-scale structure of the Universe (a vast cosmic web of galaxies, filaments, and voids) holds the key to understanding the fundamental laws of cosmology. Yet, most traditional analyses of galaxy surveys rely on summary statistics like power spectra, which strip away the rich, phase-level information encoded in the distribution of matter. Field-level inference offers a transformative alternative: instead of compressing observations into simplified metrics, it recovers the full three-dimensional density and velocity fields that shape the cosmic web, complete with rigorous uncertainty quantification.

With Manticore-Deep, we take this approach to an unprecedented scale. Building on the success of Manticore-Local, which mapped the nearby Universe with remarkable precision, Manticore-Deep extends Bayesian field-level inference to a cosmological volume of $(4 h^{-1}\;\mathrm{Gpc})^3$, reaching redshifts of $z \simeq 0.7$. This leap, an order of magnitude larger in volume, was made possible through a novel tiled inference strategy, which partitions the vast domain into manageable subvolumes while preserving the physical consistency of the reconstructed fields.

Galaxy surveys used by Manticore Deep A comparative view of the volume covered by Manticore-Local and Manticore-Deep, alongside their qualitative cosmic volume coverage

A New Approach to Cosmic Reconstruction

At the heart of Manticore-Deep lies the BORG algorithm (Bayesian Origin Reconstruction from Galaxies), a framework that infers the primordial fluctuations of the Universe and evolves them forward under the laws of gravity to reproduce the observed galaxy distribution. This method accounts for the non-linearities of structure formation, the distortions introduced by peculiar velocities, and the complexities of survey systematics, such as selection effects and observational noise.

To tackle the computational challenge of reconstructing such a vast volume, we introduced a tiled inference strategy. The parent volume, spanning $4h^{-1}\;\mathrm{Gpc}$ on each side, is divided into 64 cubic tiles, each $1h^{-1}\;\mathrm{Gpc}$ across. Each tile is inferred independently on a $256^3$ grid, with buffer regions ensuring continuity between adjacent subvolumes. After sampling, the buffers are removed, and the trimmed cores are stitched together into a global grid, yielding a statistically consistent realization of the Universe across the full volume.

The inferred initial conditions are then resimulated at higher resolution using SWIFT, a state-of-the-art N-body solver, with halos identified using HBT-HERONS. This allows us to trace the evolution of structure from the earliest fluctuations to the present day, with a level of detail that captures both the grand scale of the cosmic web and the intricate dynamics of individual galaxy clusters.

Tiling used for Manticore Deep We show here how the tiling procedure was applied to the Manticore Deep volume. Each tiles covers a piece of the volume where initial condition are inferrede independently.

Validating the Reconstruction

A reconstruction is only as good as its validation. To ensure the physical fidelity of Manticore-Deep, we subjected it to two rigorous, independent tests using observations that were not part of the inference process.

First, we projected the reconstructed 3D matter field into a convergence map and cross-correlated it with the Planck CMB lensing map. The result was a $7.4\sigma$ detection of correlated structure, a direct confirmation that the reconstructed matter field aligns with the true lensing potential of the Universe. This test is particularly powerful because it requires no assumptions about galaxy bias or redshift distributions. It is a pure, parameter-free validation of the density field.

Second, we turned to the kinetic Sunyaev–Zel’dovich (kSZ) effect, a subtle imprint on the CMB caused by the motion of galaxy clusters through the cosmic microwave background. By stacking Planck 217 GHz temperature patches at the positions of 64 750 galaxy clusters and weighting them by their line-of-sight velocities (taken from Manticore-Deep), we achieved a $3.5\sigma$ detection of the kSZ signal. This result confirms that the inferred velocity field is not only statistically consistent but also physically aligned with the true motions of clusters.

Together, these tests provide compelling evidence that Manticore-Deep accurately recovers both the density and velocity fields of the Universe, offering a faithful digital twin of the observed cosmic structure.

Key Results

Manticore-Deep delivers a wealth of insights into the large-scale structure of the Universe. The reconstructed fields are statistically consistent with the ΛCDM model, passing all key consistency tests, including the power spectrum, bispectrum, and halo mass function. This confirms that the tiled inference strategy preserves the physical properties of the initial conditions and the evolved matter fields.

Posterior mean visualization of Manticore Deep We show the posterior mean fields taken from Manticore Deep samples. Prominent cosmic structures such as the BOSS Great Wall or the CMASS supervoid are notably highlighted.

We looked more particularly at a prominent feature of the SDSS cosmic volume: the BOSS Great Wall, a colossal superstructure spanning approximately $270 h^{-1}\mathrm{Mpc}$ at a redshift of $z \simeq 0.47$, with an estimated mass of $\sim 2\times 10^{17} h^{-1}\;\mathrm{M}_\odot$.

This structure has been the subject of much debate, with some suggesting it might challenge the ΛCDM paradigm. It is completely recovered by Manticore-Deep, with a $\sim 3\sigma$ overdensity in all 15 posterior realizations, with an excess mass of $\sim 1.1 \times 10^{17} h^{-1}\;\mathrm{M}_\odot$. This result demonstrates that such massive structures are fully consistent with ΛCDM, providing a clear example of how constrained digital twins can be used to test claims of anomalous cosmic features.

Beyond individual structures, Manticore-Deep sets a new benchmark for constrained cosmological simulations at survey depth. The methods and validation frameworks developed here pave the way for future reconstructions that will leverage deeper and more detailed surveys, such as DESI, Euclid, and LSST. By establishing standardized validation metrics, like CMB lensing cross-correlation and kSZ stacking, we aim to foster a community-wide effort to compare and refine reconstructions across different methods and datasets.

The Path Forward

Manticore-Deep is just the beginning. As we look to the future, the next generation of galaxy surveys will enable even more ambitious reconstructions, pushing the boundaries of volume, resolution, and redshift depth. These advancements will allow us to probe the Universe with unprecedented precision, testing the limits of our cosmological models and uncovering new insights into the nature of dark matter, dark energy, and the fundamental laws that govern the cosmos.

The initial conditions, posterior resimulations, and reduced data products from Manticore-Deep will be made publicly available via the Manticore Project website upon publication, inviting the community to explore, validate, and build upon this work.

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