For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least $\mathcal{O}(1)$ in order to enhance the curvature power spectrum within the required number of $e$-folds between cosmic microwave background scales and PBH mass scales. Power spectrum predictions which rely on the inflaton remaining on the slow-roll attractor can fail dramatically leading to qualitatively incorrect conclusions in models like an inflection potential and misestimate the mass scale in a running mass model. We show that an optimized temporal evaluation of the Hubble slow-roll parameters to second order remains a good description for a wide range of PBH formation models where up to a $10^7$ amplification of power occurs in 10 $e$-folds or more.

• Received 29 June 2017

DOI:https://doi.org/10.1103/PhysRevD.96.063503