  In this work, we consider the corrections to the cosmological models based on
the teleparallel equivalent of general relativity induced by the non-minimal
coupling between scalar field and torsion. To determine these corrections, we
consider a power-law parametrization of the deviations between the teleparallel
equivalent of general relativity and the scalar-torsion gravity. The estimates
of the possible influence of the non-minimal coupling of the scalar field and
torsion on the background cosmological parameters and the parameters of
cosmological perturbations for the inflationary models implying linear relation
between tensor-to-scalar ratio and spectral index of the scalar perturbations
are obtained. A procedure for verifying these inflationary models based on
observational constraints on the values of cosmological perturbation parameters
is also considered.
