Primordial black holes and gravitational waves from dissipation during inflation

We study the generation of a localized peak in the primordial spectrum of curvature perturbations from a transient dissipative phase during inflation, leading to a large population of primordial black holes. The enhancement of the power spectrum occurs due to stochastic thermal noise sourcing curvature fluctuations. We solve the stochastic system of Einstein equations for many realizations of the noise and obtain the distribution for the curvature power spectrum. We then propose a method to find its expectation value using a deterministic system of differential equations. In addition, we find a single stochastic equation whose analytic solution helps to understand the main features of the spectrum. Finally, we derive a complete expression and a numerical estimate for the energy density of the stochastic background of gravitational waves induced at second order in perturbation theory. This includes the gravitational waves induced during inflation, during the subsequent radiation epoch and their mixing. Our scenario provides a novel way of generating primordial black hole dark matter with a peaked mass distribution and a detectable stochastic background of gravitational waves from inflation.