Covariant formulation of scalar-torsion gravity

TL;DR

This paper develops a covariant formulation of scalar-torsion gravity, incorporating an arbitrary function of torsion and scalar fields, ensuring Lorentz invariance and providing solutions for cosmological and spherical cases.

Contribution

It introduces a covariant approach to scalar-torsion gravity with arbitrary functions, including the spin connection as a key component, and extends the theory to multiple scalar fields.

Findings

Derived covariant field equations for the theory.

Demonstrated the automatic satisfaction of antisymmetric tetrad equations.

Provided solutions for cosmological and spherically symmetric scenarios.

Abstract

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, $f(T,\phi)$, thus encompassing the cases of $f(T)$ gravity and nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection compatible with a given tetrad. We discuss how the spin connection equation can be solved in general, and provide the cosmological and spherically symmetric examples. Finally we generalize the theory to an arbitrary number of scalar fields.