Primordial black holes and gravitational waves in teleparallel Gravity

In this paper, we consider the possible effect of teleparallel gravity on production primordial black holes (PBH) and gravitational waves (GWs). We investigate relationship between slow roll, e-folds number parameters. show that in case parameter $\delta =3$, reaches values $50$ $60$ consistency with contour plot $(r,n_{s})$ plane obtained by Planck data at $1\sigma $ $2\sigma C.L.. Furthermore, use fraction energy density variance perturbations approach to study abundance PBH. find PBH overproduction can be satisfied for specific parameters non-adiabatic curvature power spectrum some narrow parametric resonance. Moreover, explain GWs expected observations, duration preheating should bounded less or equal $2$. This bound is agreement tensor-to-scalar ratio spectral index constrained data.