Blown-up p-branes and the cosmological constant -: art. no. 013

We consider a blown-up 3-brane, with the resulting geometry R( 3,1) x S(N-1), in an infinite-volume bulk with N > 2 extra dimensions. The action on the brane includes both an Einstein term and a cosmological constant. Similar set-ups have been proposed both to reproduce the 4D gravity on the brane, and to solve the cosmological constant problem. Here we obtain a singularity-free solution to Einstein's equations everywhere in the bulk and on the brane, which allows us to address these question explicitly. One finds, however, that the proper volume of S(N-1) and the cosmological constant on the brane have to be fine-tuned relative to each other, thus the cosmological constant problem is not solved. Moreover the scalar propagator on the brane behaves four-dimensionally over a phenomenologically acceptable range only if the warp factor on the brane is huge, which aggravates the weak scale-Planck scale hierarchy problem.