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

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.

14 pages, no figures

References in corpus (9)

• The teleparallel equivalent of general relativity
• Covariant formulation of scalar-torsion gravity
• Stability of a non-minimally conformally coupled scalar field in F(T) cosmology
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Scalar-torsion theories of gravity I: general formalism and conformal transformations
• Hamiltonian formulation of teleparallel gravity
• Some aspects of reconstruction using a scalar field in f (T ) Gravity

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