Cosmological inflationary studying around the type IV singularity within f(T) gravity

Abstract

In this paper, we investigate the effects of Type IV singularity through [Formula: see text] gravity description of inflationary Universe, where [Formula: see text] denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a [Formula: see text] model according to a given Hubble rate susceptible to describe the inflationary era near the Type IV singularity. One obtains an interesting well-known [Formula: see text] model but with additional constant parameter [Formula: see text] staying as the Type IV singularity contribution. 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 at 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 [Formula: see text] trace anomaly equation, the previous result on the Type IV singularity is consolidated by the conditional instability coming from the de Sitter inflationary description of the reconstructed [Formula: see text] model. The model leads to instability strongly governed by the Type IV singularity parameter [Formula: see text] is viewed as the graceful exit from inflation. Our theoretical [Formula: see text] 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[Formula: see text]/Keck-Array data, but also shows the property of [Formula: see text] gravity in describing the early and late-time evolution of our Universe.