One-loop power spectrum in ultra slow-roll inflation and implications for primordial black hole dark matter

Understand

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory.

• We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods.
• We work in the $\delta\phi$-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff.
• The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions.