Non-Gaussian Galaxy Stochasticity and the Noise-Field Formulation

We revisit the stochastic, or noise, contributions to the galaxy density field within the effective field theory (EFT) of large-scale structure. Starting from the general, all-order expression of the EFT partition function, we elucidate how the stochastic contributions can be described by local nonlinear couplings of a single Gaussian noise field. We introduce an alternative formulation of the partition function in terms of such a noise field, and derive the corresponding field-level likelihood for biased tracers. This noise-field formulation can capture the complete set of stochastic contributions to the galaxy density at the field level in a normalized, positive-definite probability density which is suitable for numerical sampling. We illustrate this by presenting the first results of EFT-based field-level inference with non-Gaussian and density-dependent stochasticity on dark matter halos using LEFTfield.