Stochastic origin of primordial fluctuations in the Sky

We provide a study of the effects of the Effective Field Theory (EFT) generalisation of stochastic inflation on the production of primordial black holes (PBHs) in a model-independent single-field context. We demonstrate how the scalar perturbations' Infra-Red (IR) contributions and the emerging Fokker-Planck equation driving the probability distribution characterise the Langevin equations for the ``soft" modes in the quasi-de Sitter background. Both the classical-drift and quantum-diffusion-dominated regimes undergo a specific analysis of the distribution function using the stochastic-$\delta N$ formalism, which helps us to evade a no-go theorem on the PBH mass. Using the EFT-induced alterations, we evaluate the local non-Gaussian parameters in the drift-dominated limit.