Gravitation and Duality Symmetry

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.

Primordial magnetic fields constrained by CMB anisotropies and dynamo cosmology

Magneto-curvature stresses could deform magnetic field lines and this would give rise to back reaction and restoring magnetic stresses [Tsagas, PRL (2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the expansion to be slow down in spatial section of negative Riemann curvatures. From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D manifold implies negatively constant Riemannian curvature, here one applies the Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In absence of advection a fast dynamo is also obtained. Viscous and restoring forces on stretching particles decrease, as magnetic rates increase. From COBE data ($\frac{{\delta}B}{B}\approx{10^{-5}}$), one computes stretching $\frac{{\delta}V^{y}}{V^{y}}=1.5\frac{{\delta}B}{B}\approx{1.5{\times}10^{-5}}$. Zeldovich et al has computed the maximum magnetic growth rate as ${\gamma}_{max}\approx{8.0{\times}10^{-1}t^{-1}}$. From COBE data one computes a lower growth rate for the magnetic field as ${\gamma}_{COBE}\approx{6.0{\times}10^{-6}t^{-1}}$, well-within Zeldovich et al estimate. Instead of the Harrison value $B\approx{t^{{4/3}}}$ one obtains the lower primordial field $B\approx{10^{-6}t}$ which yields the $B\approx{10^{-6}G}$ at the $1s$ Big Bang time.Comment: Dept of theoretical physics-UERJ-Brasi

Analytical results for long time behavior in anomalous diffusion

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor $\lambda$. We obtain as well an exact expression for $\lambda$ for all kinds of diffusion. Moreover, we show that $\lambda$ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem