In the inflationary paradigm, the transition from quantum fluctuations to classical but stochastic density perturbations plays an important role. In particular, it implies that the open quantum system comprising the super-Hubble degrees of freedom can be described with a classical stochastic theory, the “stochastic inflation” formalism. In this framework, the short-wavelength quantum fluctuations act as a classical noise on the dynamics of the super-Hubble scales.

I will explain which quantum backreaction signatures are left by this effect on the correlation functions of primordial cosmological perturbations. I will discuss the conditions under which these can be large even at sub-Planckian energy, and I will explain which prospects it opens for probing quantum gravity effects on inflationary dynamics. As an application, I will show how the formation of primordial black holes formation from inflation is dominated by these stochastic effects.