Primordial black holes and the number of $e$-folds

Yungui Gong

Published 2017-07-30Version 1

To produce non-negligible abundance of dark matter which consists of the primordial black holes, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a big decrease in the slow-roll parameter $\epsilon$, and this will increase the number of $e$-folds. We argue that there exists either of the following problems: (1) the slow-roll approximation breaks down around the near inflection point; (2) the number of $e$-folds $N$ is much larger than $60$; (3) the enhancement of the power spectrum lasts over 60 $e$-folds and the $\mu$ distortion is large.