Blown-up p-branes and the cosmological constant

Abstract

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