Conformal transformation in $f(T)$ theories

Abstract

It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on $f(T)$ theories from observations of the solar system.

4 pages, Revision to be published

References in corpus (9)

• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Cosmological perturbations in f(T) gravity
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
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Cited by in corpus (2)

• Generalizations of teleparallel gravity and local Lorentz symmetry
• Static Solutions with Spherical Symmetry in f(T) Theories