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Abstract

Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial-physics processes and constrain models of cosmic inflation. While traditional approaches use a limited set of statistical summaries of the galaxy distribution to constrain primordial non-Gaussianity, we present a field-level approach by Bayesian forward modelling the entire three-dimensional galaxy survey. Since our method includes the entire cosmic field in the analysis, it can naturally and fully self-consistently exploit all available information in the large-scale structure, to extract information on the local non-Gaussianity parameter, f_nl. Examples include higher order statistics through correlation functions, peculiar velocity fields through redshift-space distortions, and scale-dependent galaxy bias. To illustrate the feasibility of field-level primordial non-Gaussianity inference, we present our approach using a first-order Lagrangian perturbation theory model, approximating structure growth at sufficiently large scales. We demonstrate the performance of our approach through various tests with self-consistent mock galaxy data emulating relevant features of the SDSS-III/BOSS-like survey, and additional tests with a Stage IV mock data set. These tests reveal that the method infers unbiased values of f_nl by accurately handling survey geometries, noise, and unknown galaxy biases. We demonstrate that our method can achieve constraints of σ_fnl≈8.78 for SDSS-III/BOSS-like data, indicating potential improvements of a factor ∼2.5 over current published constraints. We perform resolution studies on scales larger than ∼16h⁻¹ Mpc showing the promise of significant constraints with next-generation surveys. Furthermore, the results demonstrate that our method can consistently marginalize all nuisance parameters of the data model. The method further provides an inference of the three-dimensional primordial density field, providing opportunities to explore additional signatures of primordial physics. This first demonstration of a field-level inference pipeline demonstrates a promising complementary path forward for analysing next-generation surveys.