Primordial black holes ensued from exponential potential and coupling parameter in nonminimal derivative inflation model

Abstract

Here, Primordial Black Holes (PBHs) creation from exponential potential has been inquired, through gravitationally raised friction emanated from the nonminimal coupling between gravity and field derivative setup. Setting a two-parted exponential function of inflaton field as coupling parameter, and fine-tuning of four parameter cases of our model, we could sufficiently slow down the inflaton owing to high friction during an ultra slow-roll phase. This empowers us to achieve enough enhancement in the amplitude of curvature perturbations power spectra, via numerical solving of Mukhanov-Sasaki equation. Thereafter, we illustrate the generation of four PBHs with disparate masses in RD era, corresponding to our four parameter cases. Two specimens of these PBHs with stellar $\mathcal{O}(10)M_{\odot }$ and earth $\mathcal{O}(10^{-6})M_{\odot }$ masses can be appropriate to explicate the LIGO-VIRGO events, and the ultrashort-timescale microlensing events in OGLE data, respectively. Another two cases of PBHs have asteroid masses around $\mathcal{O}(10^{-13})M_{\odot }$ and $\mathcal{O}(10^{-15})M_{\odot }$ with abundance of $96\%$ and $95\%$ of the Dark Matter (DM) content of the universe. Furthermore, we scrutinize the induced Gravitational Waves (GWs) ensued from PBHs production in our model. Subsequently, we elucidate that their contemporary density parameter spectra $({\Omega }_{\mathrm{G}{\mathrm{W}}_0})$ for all predicted cases have acmes which lie in the sensitivity scopes of the GWs detectors, thereupon the verity of our conclusions can be verified in view of deduced data from these detectors. At length, our numerical outcomes exhibit a power-law behavior for the spectra of ${\Omega }_{\mathrm{G}{\mathrm{W}}_0}$ with respect to frequency as ${\Omega }_{\mathrm{G}{\mathrm{W}}_0}(f)\sim (f/f_c{)}^n$ in the proximity of acmes position. As well, in the infrared regime $f\ll f_c$, the log-reliant form of power index as $n=3-2/\ln (f_c/f)$ is attained.

29 pages, 5 figures

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