http://arxiv.org/abs/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 $V(\phi)$ contains a local correction term such as $V(\phi)\left[1+\varepsilon(\phi_0)\right]$. 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, $f{\rm PBH} = \Omega_{0,\rm PBH}/\Omega_{0,\rm DM} \sim O(1)$. 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 features in the inflaton potential.
S. Mishra and V. Sahni
Mon, 4 Nov 19
18/55
Comments: 28 pages, 12 figures