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

Abstract

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 ${\varphi }^{1/3}$, ${\varphi }^{2/5}$, and ${\varphi }^{2/3}$. 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 $\mathcal{O}(10)M_{\odot }$, 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 ${\Omega }_{\mathrm{G}{\mathrm{W}}_0}$ 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 ${\Omega }_{\mathrm{G}{\mathrm{W}}_0}$ with respect to frequency, given by ${\Omega }_{\mathrm{G}{\mathrm{W}}_0}(f)\sim (f/f_c{)}^n$. Additionally, in the infrared regime where $f\ll f_c$, the power index takes a log-dependent form, specifically $n=3-2/\ln (f_c/f)$.

30 pages, 8 figures

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