Why the cosmological constant problem is hard

We consider a recent proposal to solve the cosmological constant problem wi thin the context of brane world scenarios with infinite volume extra dimens ions. In such theories bulk can be supersymmetric even if brane supersymmet ry is completely broken. The bulk cosmological constant can therefore natur ally be zero. Since the volume of the extra dimensions is infinite, it migh t appear that at large distances one would measure the bulk cosmological co nstant which vanishes. We point out a caveat in this argument. In particula r, we use a concrete model, which is a generalization of the Dvali-Gabadadz e-Porrati model, to argue that in the presence of non-zero brane cosmologic al constant at large distances such a theory might become effectively four dimensional. This is due to a mass gap in the spectrum of bulk graviton mod es. In fact, the corresponding distance scale is set precisely by the brane cosmological constant. This phenomenon appears to be responsible for the f act that bulk supersymmetry does not actually protect the brane cosmologica l constant. (C) 2000 Elsevier Science B.V. All rights reserved.