Straightening the ruler: field-level inference of the BAO scale with LEFTfield

Abstract Current inferences of the BAO scale from galaxy clustering employ a reconstruction technique at fixed cosmology and bias parameters. Here, we present the first consistent joint Bayesian inference of the isotropic BAO scale, jointly varying the initial conditions as well as all bias coefficients, using the EFT-based field-level forward model LEFTfield . We apply this analysis to mock data generated at a much higher cutoff, or resolution, resulting in a significant model mismatch between mock data and the model used in the inference. We demonstrate that the remaining systematic bias in the BAO scale is below 2% for all data considered and below 1% when Eulerian bias is used for inference. Furthermore, we find that the inferred error on the BAO scale is typically 30%, and up to 50%, smaller compared to that from a replication of the standard post-reconstruction power-spectrum approach, using the same scales as in the field-level inference. The improvement in BAO scale precision grows towards smaller scales (higher k ). As a validation test, we repeat this comparison on a mock dataset that is linearly biased with respect to a 1LPT (Zel'dovich) density field, following the assumption made in standard reconstruction approaches. We find that field-level inference indeed yields the same error bar as the post-reconstruction power spectrum, which is expectd to be optimal in this case. In summary, a field-level approach to BAO not only allows for a consistent inference of the BAO scale, but promises to achieve more precise measurements on realistic, nonlinearly biased tracers as well.