Dynamical instability of brane solutions with a self-tuning cosmological constant

A five-dimensional solution to Einstein's equations coupled to a scalar fie ld has been proposed as a partial solution to the cosmological constant pro blem: the effect of arbitrary vacuum energy (tension) of a 3-brane is cance lled; however, the scalar field becomes singular at some finite proper dist ance in the extra dimension. We show that in the original model with a vani shing bulk potential for the scalar, the solution is a saddle point which i s unstable to expansion or contraction of the brane world. We construct exa ct time-dependent solutions which generalize the static solution, and demon strate that they do not conserve energy on the brane; thus they do not have an effective 4-D field theoretic description. When a bulk scalar field pot ential is added, the boundary conditions on the brane cannot be trivially s atisfied, raising hope that the self-tuning mechanism may still give some i nsight into the cosmological constant problem in this case. (C) 2000 Elsevi er Science B.V. All rights reserved.