Local Primordial Non-Gaussian Bias at the Field Level

Local primordial non-Gaussianity (LPNG) couples long-wavelength cosmological fluctuations to the short-wavelength behavior of galaxies. This coupling is encoded in bias parameters including $b_{\phi}$ and $b_{\delta\phi}$ at linear and quadratic order in the large-scale biasing framework. We perform the first field-level measurement of $b_{\phi}$ and $b_{\delta\phi}$ using Lagrangian bias and non-linear displacements from N-body simulations. We compare our field level measurements with universality predictions and separate universe results, finding qualitative consistency, but disagreement in detail. We also quantify the information on $f_{\mathrm{NL}}^{(\mathrm{loc})}$ available in the field given various assumptions on knowledge of $b_{\phi}$ at fixed initial conditions. We find that it is not possible to precisely constrain $f_{\mathrm{NL}}^{(\mathrm{loc})}$ when marginalizing over $b_{\phi} f_{\mathrm{NL}}^{(\mathrm{loc})}$ even at the field level, observing a 2-3X degradation in constraints between a linear and quadratic biasing model on perturbative field-level mocks, suggesting that a $b_{\phi}$ prior is necessary to meaningfully constrain $f_{\mathrm{NL}}^{(\mathrm{loc})}$ at the field level even in this idealized scenario. For simulated dark matter halos, the pure $f_{\mathrm{NL}}^{(\mathrm{loc})}$ constraints from both linear and quadratic field-level models appear biased when marginalizing over bias parameters including $b_{\phi}$ and $b_{\delta\phi}$ due largely to the $f_{\mathrm{NL}}^{(\mathrm{loc})} - b_\phi$ degeneracy. Our results are an important consistency test of the large-scale bias framework for LPNG and highlight the importance of physically motivated priors on LPNG bias parameters for future surveys.