Forward vs Backward: Improving BAO Constraints with Field-Level Inference

We present results of field-level inference of the baryon acoustic oscillation (BAO) scale $r_s$ on rest-frame dark matter halo catalogs. Our field-level constraint on $r_s$ is obtained by explicitly sampling the initial conditions along with the bias and noise parameters via the LEFTfield EFT-based forward model. Comparing with a standard reconstruction pipeline applied to the same data and over the same scales, the field-level constraint on the BAO scale improves by a factor of $\sim 1.2-1.4$ over standard BAO reconstruction. We point to a surprisingly simple source of the additional information.