Relaxation of the cosmological constant in a movable brane world

We present numerical evidence that a domain wall in a background with varying vacuum energy density acquires velocity in the direction of decreasing Hubble parameter. This should lead to at least a partial relaxation of the cosmological constant on the wall. hep-th/0207258 Brane-world scenarios, according to which we live on a domain wall in a higherdimensional space [1], open new avenues for thinking about the cosmological constant. Here, we want to explore feasibility of one particular mechanism that may help the “constant” to relax to a small value. The effective cosmological constant seen by an observer on the wall is determined by the local value of the Hubble parameter, H . It has long been known [2] that a domain wall in a space with zero vacuum energy will inflate, i.e. H will be nonzero. To achieve H = 0, one may introduce a negative vacuum energy in the bulk, with a value tuned precisely to compensate for the effect of the wall tension [3]. Alternatively, one can introduce a scalar field with a dilaton-like coupling to the brane, to obtain static solutions for more generic values of the tension [4]. Or, with more than two external dimensions, one may keep the bulk vacuum energy zero but assume that gravity in the bulk is so weak that the Hubble parameter induced by the wall tension is small enough to be compatible with observations [5]. Here, we want to consider a different idea. If the bulk vacuum energy varies along an extra dimension, the wall may be moving in such a way that the Hubble parameter on it starts at a large positive value but then approaches zero—or even crosses zero and becomes negative. In this way, the wall will move towards a region where two large contributions to H (one from the bulk energy, and the other from the wall tension) nearly cancel. In other words, a finely tuned solution similar to that of ref. [3] will be reached automatically in the course of the evolution. If the cancellation