Generalized exact solutions in cosmological models with non-minimal coupling of scalar field and torsion

The paper considers a method for constructing and analyzing models of cosmological inflation with a non-minimal connection between the scalar field and torsion based on generalized exact solutions. The possibility of constructing exact cosmological solutions for various physical potentials of the scalar field and arbitrary cosmological dynamics based on the proposed approach is shown. As an example, a model of cosmological inflation is considered for an open tachyon string. It is also shown that this model corresponds to modern restrictions on the values of the parameters of cosmological perturbations.