Scalar-Induced Gravitational Waves and Primordial Black Holes from a Localized Bump or Dip Feature in a Single-Field Inflationary Potential

Abstract

We study the production of scalar-induced gravitational waves and primordial black holes in a single-field inflation model with a localized bump or dip feature in the potential. Introducing such a localized feature temporarily decelerates the slow-roll inflaton, amplifying the primordial curvature power spectrum into a sharp peak. Consequently, this enhancement sources a significant stochastic background of gravitational waves and leads to abundant formation of primordial black holes. Through eight benchmark cases, we show that the predicted abundances of primordial black holes can remain compatible with current observational limits, while the corresponding gravitational wave spectra peaking across a wide range of frequencies are accessible to future gravitational wave experiments in multiple observational bands.

Figures (12)

• Figure 1: KKLT potential with a localized small bump for BP B1.
• Figure 2: Evolution of the inflaton field $\phi$ (a) and the Hubble parameter $H$ (b) as functions the number of e-folds $N - N_\mathrm{end}$ for BP B1.
• Figure 3: Evolution of the slow-roll parameters $\epsilon_{H}$ and $\eta_{H}$ as functions the number of e-folds $N - N_\mathrm{end}$ for BP B1.
• Figure 4: Primordial curvature power spectrum $\mathcal{P}_\zeta$ as a function of the e-folding number for BP B1 obtained by exactly solving the Mukhanov-Sasaki equation (blue line), compared to that given by the slow-roll approximation (yellow line).
• Figure 5: Primordial curvature power spectra as functions of the comoving wavenumber $k$ for BP B1 (green line), B2 (orange line), B3 (purple line), and B4 (magenta line). The red-, blue-, and green-shaded regions are excluded by the Planck CMB observations Planck:2018jri, the $\text{Lyman-}\alpha$ forest Bird:2010mp, and the $\mu\text{-distortion}$ of CMB Fixsen:1996nj.