Primordial black holes from a tiny bump/dip in the inflaton potential

Scalar perturbations during inflation can be substantially amplified by tiny features in the inflaton potential. A bump-like feature behaves like a local speed-breaker and lowers the speed of the scalar field, thereby locally enhancing the scalar power spectrum. A bump-like feature emerges naturally if the base inflaton potential V_b(phi) contains a local correction term such as V_b(phi)[1+ɛ(phi)] at phi=phi₀. The presence of such a localised correction term at phi₀ leads to a large peak in the curvature power spectrum and to an enhanced probability of black hole formation. Remarkably this does not significantly affect the scalar spectral index n_S and tensor to scalar ratio r on CMB scales. Consequently such models can produce higher mass primordial black holes (M_PBH>= 1 M_solar) in contrast to models with `near inflection-point potentials' in which generating higher mass black holes severely affects n_S and r. With a suitable choice of the base potential—such as the string theory based (KKLT) inflation or the α-attractor models—the amplification of primordial scalar power spectrum can be as large as 10⁷ which leads to a significant contribution of primordial black holes (PBHs) to the dark matter density today, f_PBH = Ω_{0, PBH}/Ω_0,DM ~ O(1). Interestingly, our results remain valid if the bump is replaced by a dip. In this case the base inflaton potential V_b(phi) contains a negative local correction term such as V_b(phi)[1-ɛ(phi)] at phi=phi₀ which leads to an enhanced probability of PBH formation. We conclude that primordial black holes in the mass range 10^-17 M_solar <= M_PBH <= 100 M_solar can easily form in single field inflation in the presence of small bump-like and dip-like features in the inflaton potential.