Primordial Black Holes and Slow-Roll Violation

Understand

For primordial black holes (PBH) to be the dark matter in single-field inflation, the slow-roll approximation must be violated by at least ${\cal O}(1)$ in order to enhance the curvature power spectrum within the required number of efolds between CMB 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 $10$ efolds or more.