Modified teleparallel theories of gravity

Abstract

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one can show that $f(T)$ gravity is the unique theory admitting second order field equations.

9 pages, 1 figure; some typos fixed, slightly improved notation

References in corpus (7)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• The teleparallel equivalent of general relativity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Covariance properties and regularization of conserved currents in tetrad gravity
• Teleparallel quintessence with a nonminimal coupling to a boundary term

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