Primordial black holes in scalar field inflation coupled to the Gauss-Bonnet term with fractional power-law potentials

• Published in: arXiv.org 2023-09
• Main Authors: Ashrafzadeh, Ali, Karami, Kayoomars
• Format: Article
• Language: English
• Subjects: Black holes; Curvature; Dark matter; Deceleration; Detectors; Gravitational waves; Mathematical models; Microlenses; Parameter identification; Perturbation; Power law; Scalars
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2309.16356

In this study, we investigate the formation of primordial black holes (PBHs) in a scalar field inflationary model coupled to the Gauss-Bonnet (GB) term with fractional power-law potentials. The coupling function enhances the curvature perturbations, then results in the generation of PBHs and detectable secondary gravitational waves (GWs). % We identify three separate sets of parameters for the potential functions of the form \(\phi^{1/3}\), \(\phi^{2/5}\), and \(\phi^{2/3}\). By adjusting the model parameters, we decelerate the inflaton during the ultra slow-roll (USR) phase and enhance curvature perturbations. % Our calculations predict the formation of PBHs with masses of \({\cal O}(10)M_{\odot}\), which are compatible with LIGO-Virgo observational data. Additionally, we find PBHs with masses around \({\cal O}(10^{-6})M_{\odot}\) and \({\cal O}(10^{-5})M_{\odot}\), which can explain ultrashort-timescale microlensing events in OGLE data. % Furthermore, our proposed mechanism could lead to the formation of PBHs in mass scales around \({\cal O}(10^{-14})M_{\odot}\) and \({\cal O}(10^{-13})M_{\odot}\), contributing to approximately 99\% of the dark matter in the universe. % We also study the production of secondary GWs in our model. In all cases of the model, the density parameter of secondary GWs \(\Omega_{\rm GW_0}\) exhibits peaks that intersect the sensitivity curves of GWs detectors, providing a means to verify our findings using data of these detectors. % Our numerical results demonstrate a power-law behavior for the spectra of \(\Omega_{\rm GW_0}\) with respect to frequency, given by \(\Omega_{\rm GW_0} (f) \sim (f/f_c)^{n}\). Additionally, in the infrared regime where \(f\ll f_{c}\), the power index takes a log-dependent form, specifically \(n=3-2/\ln(f_c/f)\).