Spin connection and cosmological perturbations in scalar-torsion gravity

TL;DR

This paper extends the analysis of spin connection and cosmological perturbations in scalar-torsion gravity, including non-minimal scalar field coupling and variable f, deriving consistent equations of motion.

Contribution

It generalizes previous work on spin connection in f(T) gravity to broader theories with scalar fields and non-trivial f dependencies.

Findings

Derived self-consistent equations of motion for cosmological perturbations.

Analyzed cases with and without f_{TT}=0, including non-minimal scalar coupling.

Provided solutions for the spin connection in these extended theories.

Abstract

In this paper we generalize our previous results on spin connection for the linear scalar cosmological perturbation in $f(T)$ theory to wider class of theories which includes a scalar field $\Phi$ non-minimally coupled to torsion, and allows $\Phi$-dependence of the function $f$. The case of $f_{TT}=0$, 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.