Mechanism of primordial black holes production and secondary gravitational waves in $\alpha$-attractor Galileon inflationary scenario

We study the process of the Primordial Black Holes (PBHs) production in the novel framework, namely $\alpha$-attractor Galileon inflation (G-inflation) model. In our framework, we take the Galileon function as $G(\phi)=G_{I}(\phi)\left(1+G_{II}(\phi)\right)$, where the part $G_{I}(\phi)$ is motivated from the $\alpha$-attractor inflationary scenario in its original non-canonical frame, and it ensures for the model to be consistent with the Planck 2018 observations at the CMB scales. The part $G_{II}(\phi)$ is invoked to enhance the curvature perturbations at some smaller scales which in turn gives rise to PBHs formation. By fine-tuning of the model parameters, we find three parameter sets which successfully produce a sufficiently large peak in the curvature power spectrum. We show that these parameter sets produce PBHs with masses ${\cal O}(10)M_\odot$, ${\cal O}(10^{-5})M_\odot$, and ${\cal O}(10^{-13})M_\odot$ which can explain the LIGO events, the ultrashort-timescale microlensing events in OGLE data, and around $0.98\%$ of the current Dark Matter (DM) content of the universe, respectively. Additionally, we study the secondary Gravitational Waves (GWs) in our setup and show that our model anticipates the peak of their present fractional energy density as $\Omega_{GW0} \sim 10^{-8}$ for all the three parameter sets, but at different frequencies. These predictions can be located well inside the sensitivity region of some GWs detectors, and therefore the compatibility of our model can be assessed in light of the future data. We further estimate the tilts of the included GWs spectrum in the different ranges of frequency, and confirm that spectrum follows the power-law relation $\Omega_{GW0}\sim f^{n}$ in those frequency bands.