Spin of primordial black holes from broad power spectrum: radiation dominated universe

Abstract

We perform a study to obtain the initial spin or the nondimensional Kerr parameter a* of primordial black holes (PBHs) created during the radiation dominated phase of the universe from not only nearly monochromatic but also broad curvature power spectra. Motivated by inflation and first-order phase transitions, we consider a power law shape for the curvature perturbation to model broad power spectra. We introduce a width parameter rk, the ratio of the largest and the smallest scales in which the curvature perturbation is enhanced. We find that the root mean square of a* is largest for PBHs created from locally nearly scale invariant curvature power spectra with rk ∼ 4. The upper limit is ∼ 1.1 × 10-4 for M = 1017 - 1023 g, fPBH = 1, and ∼ 1 × 10-4 for M = 1 - 100M⊙, fPBH = 0.01 and ∼ 2.2 × 10-4 even for an incredibly large mass of M = 1045 g, fPBH = 10-4.