Teleparallel Spin Connection

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.Comment: 2 pages, RevTeX, to appear in Phys. Rev D (Brief Report

Future dynamics in f(R) theories

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 adde

Electronic Griffiths phase of the d=2 Mott transition

We investigate the effects of disorder within the T=0 Brinkman-Rice (BR) scenario for the Mott metal-insulator transition (MIT) in two dimensions (2d). For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticles (QP) weights Z_{i} and strong disorder screening at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of QP parameters are strongly enhanced in the critical regime, with a distribution function P(Z) ~ Z^{\alpha-1} and \alpha tends to zero at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the MIT, in a fashion surprisingly reminiscent of the "Infinite Randomness Fixed Point" scenario for disordered quantum magnets.Comment: 4+ pages, 5 figures, final version to appear in Physical Review Letter