Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

Understand

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations.

• We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise.
• We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading.
• Using the $\Delta N$ formalism, we find the probability distribution $P(\mathcal{R})$ of the comoving curvature perturbation $\mathcal{R}$.