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

Abstract

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 Vb(ϕ) contains a local correction term such as Vb(ϕ)[1+ε(ϕ)] at ϕ=ϕ0. The presence of such a localised correction term at ϕ0 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 nS and tensor to scalar ratio r on CMB scales. Consequently such models can produce higher mass primordial black holes (MPBH⩾ 1 M⊙) in contrast to models with `near inflection-point potentials' in which generating higher mass black holes severely affects nS 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, fPBH = Ω0, PBH/Ω0,DM ∼ O(1). Interestingly, our results remain valid if the bump is replaced by a dip. In this case the base inflaton potential Vb(ϕ) contains a negative local correction term such as Vb(ϕ)[1−ε(ϕ)] at ϕ=ϕ0 which leads to an enhanced probability of PBH formation. We conclude that primordial black holes in the mass range 10−17 M⊙ ⩽ MPBH ⩽ 100 M⊙ can easily form in single field inflation in the presence of small bump-like and dip-like features in the inflaton potential.