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The Manticore Project II: Bayesian digital twins of cosmic structure across the SDSS and BOSS volumes

This paper presents Manticore-Deep, a high-resolution Bayesian field-level inference framework that reconstructs the three-dimensional cosmic density and velocity fields across a $(4~h^{-1}\mathrm{Gpc})^{3}$ volume by jointly analyzing five galaxy redshift surveys, successfully validating its physical fidelity through statistically significant cross-correlations with CMB lensing and kinematic Sunyaev-Zel'dovich effect observations.

Original authors: Stuart McAlpine, Jens Jasche, Guilhem Lavaux, Ludvig Doeser, Arthur Loureiro

Published 2026-06-10

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CC BY 4.0

Original authors: Stuart McAlpine, Jens Jasche, Guilhem Lavaux, Ludvig Doeser, Arthur Loureiro

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible web made of dark matter, with galaxies sitting on the intersections like glowing fireflies. For a long time, astronomers have tried to map this web, but they've mostly been looking at the fireflies and guessing where the web is. They've used "summary statistics"—like counting how many fireflies are in a square mile—to get a rough idea of the shape. But this throws away a lot of the story, like the specific patterns and connections between the lights.

The Manticore Project: Building a "Digital Twin" of the Universe

This paper introduces Manticore-Deep, a new way to look at the universe. Instead of just counting fireflies, the team built a "digital twin" of a massive chunk of the cosmos. Think of it like a high-definition, physics-based video game simulation that doesn't just guess where things are, but actually reconstructs the entire 3D history of how that specific region of space evolved from the Big Bang to today.

Here is how they did it, broken down simply:

1. The Puzzle and the Strategy

The team wanted to map a volume of space so huge (about 4 billion light-years across) that it would normally crash any computer trying to simulate it. It's like trying to solve a 100-million-piece puzzle all at once; your brain (or computer) would melt.

The Solution: The Tiling Strategy
To solve this, they broke the giant puzzle into 64 smaller, manageable squares (like tiles on a floor). They solved each tile independently, but with a clever trick: they made the edges of the tiles overlap slightly. This ensured that when they glued the tiles back together, the "seams" were invisible, and the cosmic web flowed smoothly from one tile to the next. This allowed them to reconstruct a volume 10 times larger than their previous attempts.

2. How They Reconstructed the Past

The team didn't just look at where galaxies are now. They used a method called Bayesian inference.

The Analogy: Imagine you walk into a room and see a pile of broken glass on the floor. You don't just guess what the vase looked like; you use the laws of physics (gravity, how glass shatters) to work backwards from the shards to figure out exactly what the original vase was.
The Application: They took the observed positions of millions of galaxies from five different surveys (like 2M++, SDSS, and BOSS) and ran them "backwards" through time. They asked: "What did the smooth, uniform soup of the early universe have to look like for gravity to pull it into the exact web of galaxies we see today?"

They didn't just find one answer. Because the data has some fuzziness, they generated 15 different possible versions (a "posterior ensemble") of what the universe could look like. All 15 versions fit the data and the laws of physics, giving them a way to measure how certain they are about every part of the map.

3. Did They Get It Right? (The "Truth" Tests)

Since they can't go back in time to check their work, they had to prove their digital twin was real using two independent "truth tests" that they didn't use to build the model.

Test A: The Cosmic Lens (CMB Lensing)
The Cosmic Microwave Background (CMB) is the "afterglow" of the Big Bang, like a giant screen behind the universe. As light from this screen travels to us, the gravity of the cosmic web bends it, distorting the image (like looking through a funhouse mirror).

The Result: They projected their reconstructed 3D web onto this screen and compared it to the actual distorted image seen by the Planck satellite.
The Score: Their digital twin matched the real distortion with a 7.4-sigma confidence level. In science, 5-sigma is the gold standard for a discovery; 7.4 is an incredibly strong confirmation that their map of the invisible dark matter is accurate.

Test B: The Wind in the Trees (Kinetic Sunyaev–Zel'dovich Effect)
Galaxy clusters are massive groups of galaxies moving through space. As they move, they drag electrons with them, which bump into the CMB light and create a tiny temperature shift (like wind blowing through trees).

The Result: They used their digital twin to predict how fast and in what direction 64,750 galaxy clusters were moving. They then checked if the actual CMB temperature map showed the "wind" patterns predicted by their twin.
The Score: They detected a signal at 3.5-sigma. This proved that their model didn't just get the location of the galaxies right; it also got the motion (velocity) right.

4. A Case Study: The BOSS Great Wall

To show off their map, they looked at the BOSS Great Wall, a massive, elongated structure of galaxies that some scientists thought might be too big to exist in our standard model of the universe (Lambda-CDM).

The Finding: In their digital twin, the BOSS Great Wall appeared as a coherent, dense structure in every single one of the 15 possible versions they generated.
The Conclusion: This proves that such a massive structure is possible within our current understanding of physics. It's not an anomaly that breaks the rules; it's just a rare but natural feature of the cosmic web.

Summary

Manticore-Deep is a massive, high-resolution, physics-based reconstruction of a huge chunk of the universe. By breaking the problem into tiles and using advanced math to work backward from today's galaxies to the early universe, they created a "digital twin" that:

Matches the laws of gravity perfectly.
Correctly predicts how the universe bends light (lensing).
Correctly predicts how galaxies move (velocity).
Confirms that even the biggest structures in the universe fit within our standard cosmological model.

It's like finally having a complete, 3D, moving map of the invisible skeleton of the universe, verified by two different types of "X-ray" vision.

Technical Summary: The Manticore Project II: Bayesian digital twins of cosmic structure across the SDSS and BOSS volumes

Problem and Motivation
Traditional analyses of the large-scale structure (LSS) of the Universe rely on low-order summary statistics, such as the two-point correlation function or power spectrum. While effective, these methods compress observational data, discarding higher-order correlations and phase information encoded in the evolved matter field. Field-level inference offers a fundamentally different approach by seeking to recover the full three-dimensional density and velocity fields that gave rise to observed galaxy distributions. While Bayesian field-level methods (e.g., BORG) have been successfully applied to the nearby Universe ( $\lesssim 200 \, h^{-1}\text{Mpc}$ ), extending these high-resolution, fully Bayesian reconstructions to cosmologically representative volumes ( $\sim \text{Gpc}^3$ ) has remained an open challenge due to computational constraints and the need to handle heterogeneous, deep survey data.

Methodology
The paper presents Manticore-Deep, a high-resolution Bayesian field-level inference spanning a comoving volume of $(4 \, h^{-1}\text{Gpc})^3$ out to redshift $z \approx 0.7$ with a resolution of $\sim 4 \, h^{-1}\text{Mpc}$ . The methodology builds upon the framework established in the companion "Manticore-Local" analysis but introduces several critical extensions:

Multi-Survey Integration: The inference jointly constrains five galaxy redshift surveys (2M++, 6dFGS, 2dFGRS, SDSS, and BOSS) within a single hierarchical Bayesian framework using the BORG algorithm.
Tiled Inference Strategy: To render the $1024^3$ voxel inference tractable, the parent domain is partitioned into a $4 \times 4 \times 4$ grid of 64 cubic tiles ( $1024 \, h^{-1}\text{Mpc}$ per side). Each tile is inferred independently on a $256^3$ grid. To mitigate boundary artifacts and ensure continuity, a buffer region ( $64 \, h^{-1}\text{Mpc}$ ) is employed where galaxies are duplicated across adjacent tiles, and the outer buffer evolves purely under the $\Lambda$ CDM prior. Post-sampling, buffer regions are discarded, and the signal-carrying cores are concatenated to form a global field.
Forward Model: The model maps primordial Gaussian white-noise initial conditions to present-day observables via a non-linear COLA-based gravity solver, redshift-space distortion modeling, and a local non-linear galaxy bias model (Sigmoid-Truncated Double Power-Law). The likelihood utilizes a Generalized Poisson distribution to account for overdispersion.
Posterior Resimulations: The inferred initial conditions are evolved using high-fidelity $N$ -body resimulations (SWIFT solver) with $4096^3$ dark matter particles to generate halo catalogs, merger trees, and lightcone outputs. This step validates the inference and provides access to higher-resolution structures.
Validation Framework: The physical fidelity is tested against two independent, template-free posterior-predictive observables not used in the inference:
1. CMB Lensing Cross-Correlation: Comparing the projected matter density from the reconstruction with the Planck PR3 CMB lensing convergence map.
2. Kinetic Sunyaev–Zel'dovich (kSZ) Stacking: Velocity-weighted stacking of galaxy clusters on the Planck 217 GHz map to detect the kSZ effect, testing the 3D velocity field.

Key Results

Statistical Consistency: The posterior realisations are statistically consistent with $\Lambda$ CDM. The inferred initial conditions exhibit Gaussian, isotropic power spectra with no detectable directional artifacts from the tiling strategy. The evolved matter power spectrum, bispectrum, and halo mass function at $z=0$ match control $\Lambda$ CDM simulations across all resolved scales.
CMB Lensing Detection: Cross-correlation between the reconstructed matter field and the Planck CMB lensing map yields a conservative cumulative detection significance of 7.4 $\sigma$ . This confirms that the reconstructed 3D density field coherently lenses the CMB in a manner consistent with the observed Universe, without requiring assumptions about galaxy bias or template fitting.
kSZ Detection: Velocity-weighted stacking of 64,750 galaxy clusters produces a kinetic Sunyaev–Zel'dovich detection at a median significance of 3.5 $\sigma$ (ranging from 2.9 to 4.3 $\sigma$ across the posterior ensemble). A model-independent split of clusters by recession/approach confirms that the inferred velocities are statistically aligned with true cluster motions.
BOSS Great Wall Case Study: The reconstruction recovers the BOSS Great Wall as a coherent overdensity. A cylinder mass analysis reveals a $\sim 3\sigma$ overdensity at an aperture radius of $\sim 100 \, h^{-1}\text{Mpc}$ relative to random lines of sight, demonstrating that such massive structures are consistent with $\Lambda$ CDM expectations when conditioned on the observed data.

Significance and Claims
The paper establishes Manticore-Deep as a new benchmark for constrained cosmological digital twins at survey depth. Its primary significance lies in:

Scalability: Demonstrating that high-resolution, fully Bayesian field-level inference can be extended from local volumes to multi-gigaparsec scales via a novel tiled strategy, preserving physical fidelity and statistical consistency.
Field-Level Validation: Introducing and applying rigorous, template-free field-level diagnostics (CMB lensing cross-correlation and kSZ stacking) that validate both the projected density and 3D velocity fields. These metrics provide reproducible, cross-method benchmarks for the next generation of LSS reconstructions, addressing the lack of object-level validation available at cosmological depths.
Physical Fidelity: Providing a causal, physics-based account of the observed large-scale structure that recovers both density and velocity information, validated against independent observational probes.

The authors conclude that these results support the robustness of the tiled inference approach and advocate for the adoption of these field-level metrics as standardised community benchmarks for future constrained simulations.

1. The Puzzle and the Strategy

2. How They Reconstructed the Past

3. Did They Get It Right? (The "Truth" Tests)

4. A Case Study: The BOSS Great Wall

Summary

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