Conformally invariant teleparallel theories of gravity

TL;DR

This paper explores conformally invariant teleparallel gravity theories, presenting new quadratic torsion models, including one that reduces to Einstein's equations under specific conditions, highlighting the framework's flexibility beyond traditional Weyl-based approaches.

Contribution

The paper introduces new conformal teleparallel gravity models, demonstrating their relation to Einstein's equations and showing the framework's broader possibilities beyond Weyl constructions.

Findings

A family of quadratic torsion conformal theories is constructed.

One theory reduces to teleparallel equivalent of GR under certain conditions.

The framework admits conformal theories beyond Weyl Lagrangian.

Abstract

We analyze the construction of conformal theories of gravity in the realm of teleparallel theories. We first present a family of conformal theories which are quadratic in the torsion tensor and are constructed out of the tetrad field and of a scalar field. For a particular value of a coupling constant, and in the gauge where the scalar field is restricted to assume a constant value, the theory reduces to the teleparallel equivalent of general relativity, and the tetrad field satisfies Einstein's equations. A second theory is formulated out of the tetrad field only, and is not equivalent to the usual Weyl Lagrangian. Therefore the latter is not the unique genuinely geometrical construction that yields a conformally invariant action. The teleparallel framework allows more possibilities for conformal theories of gravity.