Inflationary scenario driven by type IV singularity in $f(T)$ gravity

Abstract: In this paper, we investigate the effects of Type IV singularity through $f(T)$ gravity description of inflationary universe, where $T$ denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a $f(T)$ model according to a given Hubble rate susceptible to describe the inflationary era near the type IV singularity. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV Singularity, indicating that a dynamical instability of the cosmological system occurs a that point. This means that the dynamical cosmological evolution up to that point, ceases to be the final attractor since the system is abruptly interrupted. Furthermore, by considering the $f(T)$ trace anomaly equation and the slow-roll conditions, we deal with the de Sitter inflationary description of the reconstructed model. As results, the model leads to a conditional instability, view as the source of the graceful exit from inflation. Our theoretical $f(T)$ description based on slow-roll parameters not only confirms some observational data on spectral index and the scalar-to-tensor ratio from Planck data and BICEP$2$/Keck-Array data, but also shows the property of $f(T)$ gravity in describing the early and late-time evolution of our universe.