Primordial black holes from an inflationary potential valley

Primordial black holes (PBHs) could be formed if large perturbations are generated on small scales in inflation. We study a toy inflation model with a local minimum. The curvature perturbations are enhanced when the inflaton passes through the local minimum, with more efficient amplification rate than that of quasi-inflection point inflation, leading to the production of PBHs on small scales. The PBHs could comprise the total dark matter in the mass window ${10}^{16}–{10}^{20}\mathrm{g}$.

Figure 1

The configuration of the potential $V(\varphi )$ (upper panel) with parameters given by the $P_4$ set in Table 1, and the numerically calculated slow roll parameter $\eta$ (lower panel). The inset in the upper panel shows the slope of the potential around the local minimum.

Figure 2

Numerically calculated power spectrum by Bingo [63], for parameter sets $P_1$ (blue), $P_2$ (orange), $P_3$ (red), $P_4$ (purple), and $P_5$ (black) given in Table 1. The bounds are from Planck [57], COBE FIRAS data (FIRAS) [64], and a pulsar timing array (PTA) [53].

Figure 3

The fraction of PBHs as dark matter for parameter sets $P_1$ (blue), $P_2$ (orange), $P_3$ (red), $P_4$ (purple), and $P_5$ (black) in Table 1. The upper bounds are from evaporation of PBHs due to Hawking radiation (EVAP) [6, 65, 66, 67, 68, 69, 70], microlensing of stars in M31 by Subaru Hyper Suprime-Cam (HSC) [71], Optical Gravitational Lensing Experiment (OGLE) [72], North American Nanohertz Observatory for Gravitational waves (NANOGrav) [73], LIGO/Virgo’s search for subsolar mass ultracompact objects [74, 75], and CMB [76].