Primordial black holes from a type-IIB/F theory inflaton potential

Abstract

We study the possibility of the formation of primordial black holes (PBHs) using an inflaton potential constructed by stabilizing all Kähler moduli employing both the perturbative and non-perturbative corrections in the large volume scenario in type-IIB/F string theory. We further introduce a small perturbation in one of the Kähler moduli that modifies the existing potential in the field space. The effective correction in the moduli space is made by introducing a localised Gaussian bump, which induces an ultra-slow-roll feature in the inflaton potential during the early cosmological inflation. The evolution of the amplitude of the curvature power spectrum is solved numerically by using the Mukhanov-Sasaki equation, with Bunch-Davies initial conditions. The inclusion of the Gaussian bump produces a sustainable enhancement in the amplitude of curvature power spectra around $k\sim 1.12 \times 10^{9} Mpc^{-1}$ for the formation of PBHs. The abundance of PBHs ($f_{PBH}$) is calculated using the Press-Schechter formalism for different values of critical density contrast and presented in the background of contemporary $f_{PBH}$ bounds and checked for viability with existing microlensing bounds, corresponding to a mass value $10^{-6}M_\odot$ for $δ$ threshold value $δ_c=0.439$. The Hawking temperature and evaporation time are also determined for these black holes and found to be of the order of $2.78\times 10^{-15}$ GeV and $8.5\times10^{38}$ Gyr, respectively. The enhancement of curvature power spectra lies in the sensitivity region of the SKA observations, suggesting an indication that scalar-induced gravity waves may be probed in future observations.