Scalar-torsion theories of gravity I: general formalism and conformal transformations

TL;DR

This paper develops a comprehensive formalism for scalar-torsion theories of gravity, exploring their invariance properties, field equations, and relationships via conformal transformations, including generalizations to multiple scalar fields.

Contribution

It introduces a covariant framework for general scalar-torsion gravity theories, analyzes their invariance and field equations, and demonstrates their interrelations through conformal transformations and scalar field redefinitions.

Findings

Derived the general structure of field equations for scalar-torsion theories.

Showed how different theories are related by conformal transformations.

Extended the formalism to multiple scalar fields.

Abstract

We discuss the most general class of teleparallel scalar-torsion theories of gravity in their covariant formulation. The only restrictions we impose are the invariance of the action under diffeomorphisms and local Lorentz transformations, as well as vanishing direct coupling of the matter fields to the teleparallel spin connection. In this general setting we discuss the implications of local Lorentz invariance and diffeomorphism invariance and derive the general structure of the field equations. Further, we show how different theories of this class are related to each other by conformal transformations of the tetrad and redefinitions of the scalar field. We finally show how the formalism can be generalized to an arbitrary number of scalar fields, and provide a few examples.