Cosmological Predictions from the Misner Brane

Extra dimensions have a long history in gravitational physics since Kaluza [1] and Klein [2] first introduced a fifth coordinate in Einstein general relativity to account for a unified description of graviy and electromagnetism. Although string and superstring theories have reached a great deal of progress using and extending the KaluzaKlein idea, the issue of extra dimensions has never stirred theorists so much as some work carried out by Horava, Witten, Randall and Sundrum has done recently. Working in the realm of the ten-dimensional E8 × E8 heterotic string theory, Horava and Witten first showed [3] that this theory can be related to an eleven-dimensional theory on the orbifold R × S/Z2 in such a way that whereas the standard model particles are confined to the four-dimensional spacetime, gravitons propagate in the full bulk space. By simplifying the Harova-Witten framework to five dimensions, Randall and Sundrum then derived [4,5] two very interesting models where there exist two branes placed on the extra direction (which are identical to two domain walls with oposite tensions) in fivedimensional anti-de Sitter spacetime. In their first model [4], they assumed that we live in the negative-tension brane and proposed a mechanism to solve the hierarchy problem based on a small extra dimension. This scenario may have the serious problem that gravity is repulsive in the brane with negative tension [6]. Although this conclusion might be the subject of debate, one at least can certainly say that a negative tension on the physical brane brings some interpretational difficulties to the model. The second Randall-Sundrum model assumed [5] that we live in the positive-tension brane, while the other brane is moved off to infinity, so localizing gravity in one of the two three-branes only. The problem with this scenario is that the field equations in the positive-tension brane are nonlinear in the source terms [7]. Thus, the second Randall-Sundrum model avoids any possible physical effect from repulsive gravity, or at least negative brane tension in the observable universe, but unfortunately leads to noncoventional (i.e. non Friedmann) cosmology [7,8] when matter in the positive-tension brane is isotropically and homogeneously distributed, or nonconventional chargeless, nonrotating black holes [9] when the matter in that brane is assumed to collapse without rotating beyond its trapped surface. Again some controversy can arise concerning the cosmological difficulties of the second Randall-Sundrum model in particular it could be thought that the nonlinear source terms are all irrelevant at any era at which we are able to do cosmology. However, a pefectly standard Friedmann evolution appears to be a most desirable property for any cosmological model. In spite of the several attempts made in order to reconcile the nonconventional cosmological bihaviour with standard Friedmann scenario based on inserting a cosmological constant in the brane universe [10-13], within the spirit of the Randall-Sundrum approach [4,5], or on reinterpreting black-hole physics in the brane world [9], it appears that the cosmological and collapse scenarios resulting from any of the two RandallSundrum models may have serious difficulties when comparing them with current observations or theoretical requirements. On the other hand, several authors have obtained in-