Disformal Transformations in Modified Teleparallel Gravity

Abstract

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for f pT q gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others.

Foundational issues in f(T) gravity theory

“…Therefore a simple conformal transformation cannot do it, as has been noticed already some time ago [35,36]. Trying to move the factor of φ inside the torsion scalar in the Lagrangian term of φT produces the new Lorentz-breaking term with T µ ∂ µ φ. Disformal transformations did not help either [37]. A disformal transformation, with coefficients depending only on the scalar field, changes the coefficient in front of ET µ ∂ µ φ action term only by the factor of C 2 , the conformal coefficient of the transformation [37].…”

Pseudoinvariance and the extra degree of freedom inf(T)gravity

“…[11] uses the canonical Hamiltonian formalism for TEGR described in [38]. 12 While in Ref. [35] the authors claim that f (T ) gravity has n − 1 extra d.o.f.…”

“…• n secondary constraints G (2) µ due to the diffeomorphism invariance (same constraints as in GR). 12 In Ref. [38] From the whole set of primary and secondary constraints of the theory, there are only two non-vanishing Poisson brackets.…”

“…is governed by z ∂g/∂z − z ∂g/∂z. On the other hand, the infinitesimal Lorentz transformation of L T EGR can be obtained from the expression (12), rewritten as L T EGR = −ER + 2∂ µ (ET µ ). In varying it, we must take into account that ER is locally invariant under Lorentz transformations of the tetrad -it depends exclusively on the metric-.…”

“…µ due to the diffeomorphism invariance (same constraints as in GR). 12 In Ref. [38] the TEGR Lagrangian was expressed in the form…”