Ju l 2 00 9 Conservation of Energy – Momentum in Teleparallel Gravity

In a well-known paper [1] V.C. de Andrade, L. C. T. Guillen and J.G. Pereira defined a conserved gauge current hj ρ a , however they stated that: " This is, we believe the farthest one can go in the direction of a tensorial definition for the energy and momentum of the gravitational field. The lack of local Lorentz covariance can be considered as the teleparallel manifestation of the pseudotensor character of the gravi-tational energy–momentum density in general relativity.. . ". Well, we believe that they stopped just less than an inch before giving such a ten-sorial definition, and furthermore that the resulting energy–momentum tensor has zero trace and can be made symmetric, as a matter of fact it is just j (νρ) , and together with the energy–momentum tensor of material fields it obeys a natural conservation equation for teleparallel manifolds. Some important consequences are obtained specially in the last section concerning the possibility of explaining the acceleration of the universe expansion without any need of a cosmological constant. 1 The energy–momentum tensor We follow most of the conventions and notations of references [1] and [2]. However one difference is that we stick to consider the lagragian density of the gravitational field to be proportional to + o R (as it is usually accepted) instead of being proportional to − o R as is done in [1]. Any further difference will be made it explicit. Anyway let us at least remember that greek indices 1