Cosmological inflationary scenarios in modified teleparallel theory of gravity assisted by scalar field

In this paper, we investigate cosmological inflationary dynamic powered by the scalar field through the modified [Formula: see text] theory of gravity where T is the scalar torsion. In approach similar to some works in the literature, the scalar field [Formula: see text] is built from the function [Formula: see text] leading to what we call Brans–Dike construction. Under this consideration, the Friedmann equations lead to a differential equation depending on scalar field and Hubble parameter and its analytical resolution is provided for the de Sitter evolution on one hand and for the power-law expansion on the other. From the Klein Gordon equation, the scalar field potential is found and leads to spectral index and the tensor-to-scalar ratio which agree with Planck Satellite 2013 data and other observational data. Inversely, the chaotic inflation is addressed by considering massive scalar field potential. For suitable choice of the free parameters, the results promote quasi-de-Sitter evolution with spectral index and tensor-to-scalar ratio in agreement with both Planck Satellite and BICEP2 experiment observational data. The approach followed in this work constitutes a successful way to reconstruct viable cosmological [Formula: see text] models which mimic well the spirit of the modified theories of gravity.