Variational Problem and Bigravity Nature of Modified Teleparallel Theories

Abstract

We consider the variational principle in the covariant formulation of modified teleparallel theories with second order field equations. We vary the action with respect to the spin connection and obtain a consistency condition relating the spin connection with the tetrad. We argue that since the spin connection can be calculated using an additional reference tetrad, modified teleparallel theories can be interpreted as effectively bigravity theories. We conclude with discussion about the relation of our results and those obtained in the usual, non-covariant, formulation of teleparallel theories and present the solution to the problem of choosing the tetrad in $f(T)$ gravity theories.

15 pages, v3: significantly updated version including new results

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Cited by in corpus (9)

• Teleparallel Gravity: From Theory to Cosmology
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• Covariant formulation of scalar-torsion gravity
• New classes of modified teleparallel gravity models
• Modified teleparallel theories of gravity in symmetric spacetimes
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• $H_0$ Tension and the Phantom Regime: A Case Study In Terms of an Infrared $f(T)$ Gravity
• Junction Conditions for F(T) Gravity from a Variational Principle