Reconstructing the largest scales of the Universe with field-level inference applied to the Quaia Quasar Catalogue

TL;DR

This work applies the Bayesian Origin Reconstruction from Galaxies (BORG) field-level inference framework to the Quaia Gaia-unWISE quasar catalogue to recover the initial conditions and present-day matter distribution over an unprecedented comoving volume of $V=(10\,h^{-1}\,\text{Gpc})^{3}$ at a resolution of $L_{\rm vox}=39.1\,h^{-1}\text{Mpc}$. By forward-modeling structure formation with Lagrangian perturbation theory, including light-cone effects, redshift-space distortions, quasar bias, and survey selection, the authors reconstruct three-dimensional density and velocity fields traced by sparsely distributed quasars and quantify uncertainties with an ensemble of MCMC samples. They validate the reconstructions via power spectra, bispectra, and velocity-field tests, and detect a cross-correlation with Planck CMB lensing at up to $\sim 4\sigma$, providing external validation of the large-scale structures inferred from Quaia. The results demonstrate the feasibility and value of field-level cosmology using quasar surveys, enabling future probes of ISW effects, primordial non-Gaussianity, and other ultra-large-scale physics with upcoming deep, wide-area datasets.

Abstract

The recently released Quaia quasar catalogue, with its broad redshift range and all-sky coverage, enables unprecedented three-dimensional reconstructions of matter across cosmic time. In this work, we apply the field-level inference algorithm BORG to the Quaia catalogues to reconstruct the initial conditions and present-day matter distribution of the Universe. We employ a physics-based forward model of large-scale structure using Lagrangian perturbation theory, incorporating light-cone effects, redshift-space distortions, quasar bias, and survey selection effects. This approach enables a detailed and physically motivated inference of the three-dimensional density field and initial conditions over the entire cosmic volume considered. We analyse both the G < 20.0 (Quaia Clean) and G < 20.5 (Quaia Deep) samples, where G denotes the Gaia broad optical-band magnitude, imposing conservative sky cuts to ensure robustness against foreground contamination. The resulting reconstructions span a comoving volume of (10h^{-1} Gpc)^3 with a maximum spatial resolution of 39.1 h^{-1}Mpc, making this the largest field-level reconstruction of the observable Universe in terms of comoving volume to date. We validate our reconstructions through a range of internal and external consistency checks, including the cross-correlation of the inferred density fields with Planck CMB lensing, where we detect a signal at ~4σsignificance. Beyond delivering high-fidelity data products, including posterior maps of initial conditions, present-day dark matter, and velocity fields, this work establishes a framework for exploiting quasar surveys in field-level cosmology.

Figures (22)

• Figure 1: Distribution of quasars and inferred fields from the Quaia Deep Cut quasar catalog, which provide an overview of the outcomes of the BORG analysis. The main panel shows the survey volume coverage, comparing Quaia (black dots) with SDSS-III (gray range) and the Euclid spectroscopic range (yellow range). The panels on the right-hand side shows the corresponding inferred fields of the black inset; the bottom-right panel shows the mean inferred initial conditions ($\delta_{\mathrm{IC}}$), centre-right the dark matter density field ($\delta_{\rm{m}}$), and upper-right the radial velocity field ($v_{\rm r}$). The imprint of the survey edge in the panels highlights BORG’s ability to account for systematics across the ensemble of the MCMC samples. In the dark matter density panel, we overlay the quasars, illustrating the match between input data and inferred structures, which demonstrates the ability of the BORG to recover the large-scale structure from sparsely distributed quasars. The thickness of the slice shown here is approximately $39\, h^{-1}\,\text{Mpc}$; the unit for the radial velocity field is $\rm{km\,s^{-1}}$.
• Figure 2: Angular selection function, or completeness, for the (a)Quaia Clean ($G<20.0$) sample, as estimated by SF24, and the (b)Quaia Deep Cut ($G<20.5$) sample. Both maps are shown in celestial coordinates. Note that for the Quaia Deep Cut we removed the Large and Small Magellanic Clouds and applied a completeness cut of $0.5$. See text for details.
• Figure 3: Radial selection function for the Quaia Clean ($G<20.0$) sample (purple) and the Quaia Deep Cut ($G<20.5$) sample (teal). The shaded region outlines the range used in the sub-catalogues in our analysis.
• Figure 4: Evolution of the comoving distance mean error as a function of redshift compared to the smallest scale considered in this work, $L_{\rm vox}^{256}$. This shows that, on average, the error on the SPZ redshifts is well below the voxel resolution and will not affect our reconstructions.
• Figure 5: Flow chart of the forward model adopted in this paper, summarising the steps from initial conditions to late-time observables as described in Section \ref{['ssect:forward_model']}. The model begins with a Gaussian white-noise field, which is modulated by the primordial power spectrum to generate the initial gravitational potential. The resulting density field is evolved using Lagrangian Perturbation Theory (LPT) to predict matter and velocity fields at late times. Observational effects, including redshift-space distortions, light-cone effects, and survey selection functions, are then applied to yield the final predicted galaxy distribution.