Conformal transformation in $f(T)$ theories

Details Conformal transformation in $f(T)$ theories Conformal transformation in $f(T)$ theories

2010-10-07

arxiv.org/abs/1010.1376v3

Europhys.Lett.93:60001,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, Revision to be published

Scientific paper

10.1209/0295-5075/93/60001

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.

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