Primordial non-Gaussianity (PNG) is a common prediction of a wide class of inflationary models. Equilateral-type PNG, generically predicted by single-field inflationary models with higher-derivative interactions, imprints subtle but measurable signatures on the large-scale distribution of matter. An important parameter of these imprints is the PNG-induced bias coefficient $b_{\psi }$, which quantifies how the abundance and clustering of dark matter halos and galaxies respond to mode coupling in the initial conditions. Measuring $b_{\psi }$ is important for constraining equilateral PNG, yet it is notoriously challenging due to its degeneracy with Gaussian scale-dependent bias contributions. In this work, we present the first precision measurements of equilateral $b_{\psi }$ for dark matter halos using effective field theory at the field level. We show that this approach disentangles PNG effects from those of the Gaussian bias by virtue of noise variance cancellation. We compare our results with the phenomenological predictions based on the peak-background split model, finding some agreement at the qualitative level on the redshift and mass dependence, but poor agreement at the quantitative level. We present a fitting formula for $b_{\psi }$ as a function of the linear bias, which can be used to set priors in PNG searches with ongoing and future galaxy surveys.

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• Inflation
• Large scale structure of the Universe