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 ${\phi }^{1\mathrm{/}3}$, ${\phi }^{2\mathrm{/}5}$, and ${\phi }^{2\mathrm{/}3}$. 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 $\mathcal{O}(10)M_{\odot }$, which are compatible with LIGO-Virgo observational data. Additionally, we find PBHs with masses around $\mathcal{O}({10}^{-6})M_{\odot }$ and $\mathcal{O}({10}^{-5})M_{\odot }$, 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 $\mathcal{O}({10}^{-14})M_{\odot }$ and $\mathcal{O}({10}^{-13})M_{\odot }$, 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 ${\mathrm{\Omega }}_{\mathrm{G}{\mathrm{W}}_0}$ 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 ${\mathrm{\Omega }}_{\mathrm{G}{\mathrm{W}}_0}$ with respect to frequency, given by ${\mathrm{\Omega }}_{\mathrm{G}{\mathrm{W}}_0}(f)\sim (f\mathrm{/}{f}_c{)}^n$. Additionally, in the infrared regime where $f\ll f_c$, the power index takes a log-dependent form, specifically $n=3-2\mathrm{/}\ln (f_c\mathrm{/}f)$.