Non-Gaussianity and Secondary Gravitational Waves from Primordial Black Holes Production in $\alpha$-attractor Inflation

We study the non-Gaussianity and secondary Gravitational Waves (GWs) in the process of the Primordial Black Holes (PBHs) production from inflation. In our work, we focus on the $\alpha$-attractor inflation model in which a tiny bump in the inflaton potential enhances the amplitude of the curvature perturbations at some scales and consequently leads to the PBHs production with different mass scales. We implement the computational code BINGO which calculates the non-Gaussianity parameter in different triangle configurations. Our examination implies that in this setup, the non-Gaussianity gets amplified significantly in the equilateral shape around the scales in which the power spectrum of the scalar perturbations undergoes a sharp declination. The imprints of these non-Gaussianities can be probed in the scales corresponding to the BBN and $\mu$-distortion events, or in smaller scales, and detection of such signatures in the future observations may confirm the idea of our model for the generation of PBHs or rule it out. Moreover, we investigate the secondary GWs in this framework and show that in our model, the peak of the present fractional energy density is obtained as $\Omega_{\rm GW0} \sim 10^{-8}$ at different frequencies which depends on the model parameters. These results lie well within the sensitivity region of some GWs detectors at some frequencies, and therefore the observational compatibility of our model can be evaluated by the forthcoming data from these detectors. We further provide some estimations for the tilts of the induced GWs spectrum in the different intervals of frequency, and demonstrate that the spectrum obeys the power-law relation $\Omega_{\rm GW0}\sim f^{n}$ in those frequency bands.