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

Abstract: We present Manticore-Deep, a high-resolution Bayesian field-level inference of cosmic large-scale structure spanning a comoving volume of $(4~h^{-1}\mathrm{Gpc})^{3}$ out to $z \approx 0.7$, at ${\sim}4$~Mpc/h resolution. Building on the inference framework established in the companion Manticore-Local analysis (P1), Manticore-Deep jointly constrains five galaxy redshift surveys (2M++, 6dFGS, 2dFGRS, SDSS, and BOSS) within a single hierarchical Bayesian framework using the BORG algorithm. The method infers initial conditions that are evolved forward under gravitational dynamics, delivering a full posterior ensemble of three-dimensional density and velocity fields that causally reproduce the observed large-scale structure. A novel tiled inference strategy makes this computation feasible, extending the reconstructed volume by more than an order of magnitude beyond P1. The posterior realisations are statistically consistent with LCDM, exhibiting Gaussian, isotropic initial conditions and evolving into late-time structures that reproduce the expected $z=0$ matter power spectrum, bispectrum, and halo mass function across the resolved scales tested. We validate the physical fidelity of the reconstruction through two independent, template-free posterior-predictive tests against observations not used in the inference. Cross-correlation of the reconstructed matter field with the Planck PR3 CMB lensing map yields a conservative cumulative detection significance of 7.4$σ$, while velocity-weighted stacking of $64750$ galaxy clusters on the Planck 217~GHz map produces a kSZ detection at $3.5σ$, with a model-independent approach--recession split confirming that the inferred velocities are statistically aligned with the true cluster motions. As a case study, we show that the BOSS Great Wall is recovered as a ${\sim}3σ$ overdensity consistent with LCDM across all posterior realisations.