Euclid: Field-level inference of primordial non-Gaussianity and cosmic initial conditions

A primary target of the Euclid space mission is to constrain early-universe physics by searching for deviations from a primordial Gaussian random field. A significant detection of primordial non-Gaussianity would rule out the simplest models of cosmic inflation and transform our understanding of the origin of the Universe. This paper forecasts how well field-level inference of galaxy redshift surveys can constrain the amplitude of local primordial non-Gaussianity, f(loca)l(NL), within a Bayesian hierarchical framework, in the upcoming Euclid data. We designed and simulated mock datasets and performed Markov chain Monte Carlo analyses using a full-field forward modelling approach. By including the formation history of the cosmic matter field in the analysis, the method takes into account all available probes of primordial non-Gaussianity, and goes beyond statistical summary estimators of f(NL)(local). Probes include, for example, two-point and higher-order statistics, peculiar velocity fields, and scale-dependent galaxy biases. Furthermore, the method simultaneously handles systematic survey effects, such as selection effects, survey geometries, and galaxy biases. The forecast shows that, using simulated Euclid data, the method can achieve a precision of sigma(f(NL)(local)) = 2.6 (68.3% confidence level), assuming a grid resolution of Delta L = 31.25 h(-1) Mpc and a cut-off scale of k(NF) = 0.1 h Mpc(-1). We also provide data products, including realistic simulations with non-zero values of f(NL)(local) and maps of adiabatic curvature fluctuations. The results underscore the feasibility and advantages of field-level inference to constrain f(NL)(local) in galaxy redshift surveys. Our approach consistently captures all the information available in the large-scale structure to constrain f(NL)(local), and resolves the degeneracy between early-universe physics and late-time gravitational effects, while mitigating the impact of systematic and observational effects.