Scalar-torsion theories of gravity II: $L(T, X, Y, \phi)$ theory

TL;DR

This paper develops a class of Lorentz invariant scalar-tensor teleparallel gravity theories with a complex Lagrangian, deriving their field equations, analyzing their consistency, and exploring their behavior under conformal transformations.

Contribution

It introduces a new class of scalar-torsion gravity theories with explicit relations between spin connection and tetrad equations, and studies their transformation properties.

Findings

Derived the field equations for the $L(T, X, Y, )$ theory.

Established the relation between spin connection and tetrad field equations.

Showed conformal transformations map these theories onto each other.

Abstract

We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such transformations map different theories in this class onto each other.