Field-Level Inference from Galaxies: BAO Reconstruction

Abstract

Baryon acoustic oscillations (BAO) underpin the key cosmological results from modern spectroscopic galaxy surveys, but nonlinear gravitational evolution limits the precision achievable with traditional analysis methods. To overcome this, we develop field-level inference for BAO, first reconstructing the initial linear density field and then fitting the BAO signal therein. We benchmark three reconstruction methods: (i) traditional reconstruction based on the Zel'dovich approximation, (ii) explicit field-level inference using differentiable forward modeling with hybrid effective field theory, and (iii) implicit field-level inference using a convolutional neural network to augment traditional reconstruction. Using DESI-like Luminous Red Galaxy (LRG) and Bright Galaxy Survey (BGS) catalogs, we find that field-level approaches significantly sharpen the BAO feature relative to traditional reconstruction. For LRGs, explicit field-level inference improves constraints on the BAO scale parameters ($α_{\rm iso}, α_{\rm ap}$) by 26%, while implicit inference improves constraints by 35%, corresponding to a 2.4$\times$ improvement in figure of merit. For the higher-density, lower-redshift BGS sample, field-level inference enables information extraction from smaller scales, yielding an improvement in constraints of up to 46%, corresponding to a 3.2$\times$ improvement in figure of merit. Crucially, we address longstanding concerns regarding the robustness of field-level reconstruction by leveraging 1,000 mock realizations to perform extensive coverage tests. Our results are both unbiased and statistically well-calibrated, maintaining nominal coverage even when using tight simulation-informed priors and under model misspecification.

Figures (14)

• Figure 1: Distribution of mock galaxies. Number of central (teal), satellite (peach), and all (gray) galaxies as a function of host halo mass for LRGs (left) and BGS (right).
• Figure 2: Illustration of Reconstructions. Given the observed galaxy field (left), we perform reconstruction using three different methods of increasing quality from left to right: traditional BAO reconstruction, explicit field-level inference, and implicit field level inference. The reconstruction quality can be seen to improve going from traditional to explicit field-level to implicit field-level. All images are 2D projections along a direction perpendicular to the line-of-sight of thickness $125\,{\rm Mpc}/h$. The colorbar limits are set based on the extreme values of the linear field. The linear bias has been scaled out of the traditional reconstruction to enable apples-to-apples comparison.
• Figure 3: Cross-correlation coefficient$r$ of traditional (black), explicit field-level (blue), and implicit field-level (gold) reconstruction, in order of increasing quality.
• Figure 4: Monopole and Quadrupole of reconstructed fields for traditional (black), explicit field-level (blue), and implicit field-level (gold) reconstruction. The top panel shows the monopole (solid model fit, circular data points) and quadrupole (dotted model fit, crossed data points). The lower panels show the residuals divided by the diagonal covariance, showing sub-percent quality of fit.
• Figure 5: BAO wiggle signal-to-noise of reconstructed fields for traditional (black), explicit field-level (blue), and implicit field-level (gold) reconstruction. Each panel shows the power divided by the root Gaussian covariance. The small scale wiggles in the monopole (top panel) are best reconstructed by implicit inference, followed by explicit. The quadrupole (lower panel) has pronounced wiggles on large scales for traditional reconstruction, but is close to zero in the field-level cases which remove RSD by design.