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Dynamical Instability of Brane Solutions with a Self-Tuning Cosmological Constant

P. Binetruy·J. M. Cline·C. Grojean
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Abstract

A five-dimensional solution to Einstein's equations coupled to a scalar field has been proposed as a partial solution to the cosmological constant problem: the effect of arbitrary vacuum energy (tension) of a 3-brane is cancelled; however, the scalar field becomes singular at some finite proper distance in the extra dimension. We show that in the original model with a vanishing bulk potential for the scalar, the solution is a saddle point which is unstable to expansion or contraction of the brane world. We construct exact time-dependent solutions which generalize the static solution, and demonstrate 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 potential is added, the boundary conditions on the brane cannot be trivially satisfied, raising hope that the self-tuning mechanism may still give some insight into the cosmological constant problem in this case.

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P. Binetruy, J. M. Cline, C. Grojean. 2000-07-04. Dynamical Instability of Brane Solutions with a Self-Tuning Cosmological Constant. https://doi.org/10.1016/s0370-2693(00)00932-1

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