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The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R) = R + \alpha R^{n}$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $\omega < -1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R) = R + \alpha R^n $. We also show that FLRW dust solutions with $f''<0$ do not necessarily lead to singularity., Comment: 12 pages, 8 figures. V2: Generality and implications of the results are emphasized, connection with the recent literature improved, typos corrected, references added

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than teleparallel gravity or general relativity., Comment: 7 pages, no figures. Version 2: minor presentation changes, references added. Accepted for publication in Int. J. Mod. Phys. D

Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg-Salam theory are present, and a few others which are nevertheless consistent within the model., Comment: 11 pages; revtex; title and PACS have been changed; comments included in the manuscript

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the M{\o}ller's canonical energy-momentum density of the gravitational field., Comment: RevTeX, 4 pages, no figures, to appear in Phys. Rev. Lett

Relying upon the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the original Kaluza-Klein theory is developed. In this model, only the internal space (fiber) turns out to be five dimensional, spacetime being kept always four dimensional. A five-dimensional translational gauge theory is obtained which unifies, in the sense of Kaluza-Klein theories, gravitational and electromagnetic interactions., Comment: 5 pages, no figures, RevTeX; title and presentation changes, a new paragraph and references added, version to appear in Phys. Rev. D

The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square--root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account., Comment: 8 pages, RevTeX Style, no figures, changed presentation -- now restricted to fields of spin 0, 1/2 and 1 -- some references added

In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, to produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory., Comment: RevTeX, 12 pages, minor changes, some references added, version to appear in Int. J. Mod. Phys. D