Primordial Black Holes from a tiny bump/dip in the Inflaton potential

• Published in: arXiv.org 2020-03
• Main Authors: Mishra, Swagat S, Sahni, Varun
• Format: Article
• Language: English
• Subjects: Amplification; Dark matter; String theory; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1911.00057

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 \(V_b(\phi)\left[1+\varepsilon(\phi)\right]\) at \(\phi=\phi_0\). The presence of such a localised correction term at \(\phi_0\) 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 (\(M_{\rm PBH}\geq 1 M_{\odot}\)) 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 \(\alpha\)-attractor models - the amplification of primordial scalar power spectrum can be as large as \(10^7\) which leads to a significant contribution of primordial black holes (PBHs) to the dark matter density today, \(f_{\rm PBH} = \Omega_{0,\rm PBH}/\Omega_{0,\rm DM} \sim O(1)\). 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 \(V_b(\phi)\left[1-\varepsilon(\phi)\right]\) at \(\phi=\phi_0\) which leads to an enhanced probability of PBH formation. We conclude that primordial black holes in the mass range \(10^{-17} M_{\odot} \leq M_{\rm PBH} \leq 100\, M_{\odot}\) can easily form in single field inflation in the presence of small bump-like and dip-like features in the inflaton potential.