Primordial black holes and gravitational waves in teleparallel Gravity

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In this paper, we consider the possible effect of the teleparallel gravity on the production of the primordial black holes (PBH) and on the gravitational waves (GWs).

• We investigate the relationship between the slow roll, the e-folds number and the teleparallel parameters.
• We show that in the case of the teleparallel parameter $\delta =3$, the e-folds number reaches the values $50$ and $60$ in consistency with the contour plot of the $(r,n_{s})$ plane obtained by Planck data at $1\sigma $ and $2\sigma $ C.L..
• Furthermore, we use the fraction of the energy density and the variance of the density perturbations approach to study the abundance of the production PBH.