How I stop worrying about non-universality and $b_\phi$: Constraining local $f_{\rm NL}$ with $b_\phi$ priors from HOD posteriors

Abstract

Local primordial non-Gaussianity (local PNG) induces a scale-dependent contribution to galaxy clustering proportional to $f_{\rm NL}\,b_\phi$, where $f_{\rm NL}$ is the local PNG amplitude and $b_\phi$ encodes the galaxy response to a long-wavelength primordial potential perturbation. Uncertainty in $b_\phi$ is the dominant obstacle to precise, robust constraints on $f_{\rm NL}$ from galaxy surveys. We translate small-scale clustering constraints on the galaxy--halo connection into priors on $b_\phi$: sampling the posterior of a halo occupation distribution (HOD) model fit to the DESI EDR, we generate mocks from which we measure $b_\phi$ and construct its prior. Validating against additional mocks with different local PNG amplitudes, we show that the method recovers unbiased $f_{\rm NL}$, even in the presence of assembly bias.