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

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 $n=3-2/\ln(f_c/f)$.