Abstract
In this paper, we generalize our previous results on spin connection for the linear scalar cosmological perturbation in [Formula: see text] theory to a wider class of theories which includes a scalar field [Formula: see text] non-minimally coupled to torsion, and allows [Formula: see text]-dependence of the function [Formula: see text]. The case of [Formula: see text], with a scalar field non-minimally coupled to torsion, needs a special treatment. In both considered cases we derive self-consistent equations of motion for cosmological perturbation using a solution for non-trivial spin connection.
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