Reconstruction of f(T) cosmological singular model unifying early and late-time eras with radiation-matter-dominated epochs

In this paper, we consider two interesting cosmological models characterized by two expressions of the Hubble parameter and as goal, we realize the unification of the early-time and the late-time acceleration eras with the radiation- and matter-dominated eras, and this, in the context of f(T) theory of gravity. The particularity here is that the first model ensures just the unification of the early- and late-time eras with the matter-dominated era without the account of the radiation era, while the second model guarantees the unification of all the eras, namely, the early time, the radiation- and matter-dominated eras, and the late-time acceleration era. For each model, we point out two type IV singularities, the first occurring at the end of the inflationary era and the second at the end of the matter-dominated era. For the first model, the Hubble radius is introduced and three different expressions are taken into account: the first for the inflationary era, the second for the matter-dominated era and the third for the dark energy-dominated era. Hence, the algebraic f(T) is reconstructed for the three eras. Attention is attached to the inflationary era by calculating the corresponding two first slow-roll parameters and challenging them with recent Planck and BICEP2/Keck-Array observational data, and the results show the consistency of the reconstructed inflationary model. For the second model, we note a similarity with the first model, concerning the inflationary, matter-dominated and late-time acceleration eras. Then, we just perform the reconstruction of f(T), which is able to realize the radiation-dominated era.