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

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.Comment: 4 pages, Revision to be publishe

Existence of relativistic stars in f(T) gravity

We examine the existence of relativistic stars in f(T) modified gravity and explicitly construct several classes of static perfect fluid solutions. We derive the conservation equation from the complete f(T) gravity field equations and present the differences with its teleparallel counterpart. Firstly, we choose the tetrad field in the diagonal gauge and study the resulting field equations. Some exact solutions are explicitly constructed and it is noted that these solutions have to give a constant torsion scalar. Next, we choose a non diagonal tetrad field which results in field equations similar to those of general relativity. For specific models we are able to construct exact solutions of these field equations. Among those new classes of solutions, we find negative pressure solutions, and an interesting class of polynomial solutions.Comment: 19 pages; substantially revised and extended version, off diagonal tetrad discussion adde

G-essence with Yukawa interactions

We study the g-essence model with Yukawa interactions between a scalar field $\phi$ and a Dirac field $\psi$. For the homogeneous, isotropic and flat Friedmann-Robertson-Walker universe filled with the such g-essence, the exact solution of the model is found. Moreover, we reconstruct the corresponding scalar and fermionic potentials which describe the coupled dynamics of the scalar and fermionic fields. It is shown that some particular g-essence models with Yukawa interactions correspond to the usual and generalized Chaplygin gas unified models of dark energy and dark matter. Also we present some scalar-fermionic Dirac-Born-Infeld models corresponding g-essence models with Yukawa interactions which again describe the unified dark energy-dark matter system.Comment: 13 page