Full-shape analysis with simulation-based priors: Constraints on single field inflation from BOSS

Perturbative, or effective field theory (EFT)-based, full-shape analyses of galaxy clustering data involve ``nuisance parameters'' to capture various observational effects such as the galaxy-dark matter connection (galaxy bias). We present an efficient approach to set informative physically motivated priors on these parameters. We extract these priors from simulated galaxy catalogs based on halo occupation distribution (HOD) models. First, we build a joint distribution between EFT galaxy bias and HOD parameters from a set of 10,500 HOD mock catalogs. We use the field level EFT technique that allows for cosmic variance cancellation, enabling a precision calibration of EFT parameters from computationally inexpensive small-volume simulations. Second, we use neural density estimators -- normalizing flows -- to model the marginal probability density of the EFT parameters, which can be used as a prior distribution in full shape analyses. As a first application, we use our HOD-based priors in a new analysis of galaxy power spectra and bispectra from the BOSS survey in the context of single field primordial non-Gaussianity. We find that our priors lead to a reduction of the posterior volume of bias parameters by an order of magnitude. We also find $f_{\rm NL}^{\rm equil} = 320\pm 300$ and $f_{\rm NL}^{\rm ortho} = 100\pm 130$ (at 68\% CL) in a combined two-template analysis, representing a $\approx 40\%$ improvement in constraints on single field primordial non-Gaussianity, equivalent to doubling the survey volume.