Gravitational Lorentz violations and adjustment of the cosmological constant in asymmetrically warped spacetimes

We investigate spacetimes in which the speed of light along flat 4D section s varies over the extra dimensions due to different warp factors for the sp ace and the time coordinates ("asymmetrically warped" spacetimes). The main property of such spaces is that while the induced metric is flat, implying Lorentz invariant particle physics on a brane, bulk gravitational effects will cause apparent violations of Lorentz invariance and of causality from the brane observer's point of view. An important experimentally verifiable consequence of this is that gravitational waves may travel with a speed dif ferent from the speed of light on the brane, and possibly even faster. We f ind the most general spacetimes of this sort, which are given by AdS-Schwar zschild or AdS-Reissner-Nordstrom black holes, assuming the simplest possib le sources in the bulk, Due to the gravitational Lorentz violations these m odels do not have an ordinary Lorentz invariant effective description, and thus provide a possible way around Weinberg's no-go theorem for the adjustm ent of the cosmological constant, Indeed we show that the cosmological cons tant may relax in such theories by the adjustment of the mass and the charg e of the black hole. The black hole singularity in these solutions can be p rotected by a horizon, but the existence of a horizon requires some exotic energy densities on the brane, We investigate the cosmological expansion of these models and speculate that it may provide an explanation for the acce lerating Universe, provided that the timescale for the adjustment is shorte r than the Hubble time. In this case the accelerating Universe would be a m anifestation of gravitational Lorentz violations in extra dimensions. Publi shed by Elsevier Science B.V.