(De)stabilization of an extra dimension due to a Casimir force - art. no. 124020

We study the stabilization of one spatial dimension in (p + 1 + 1)-dimensio nal spacetime in the presence of p-dimensional brane(s), a bulk cosmologica l constant and the Casimir force generated by a conformally coupled scalar field. We find general static solutions to the metric which require the fin e-tuning of the inter-brane distance and the bulk cosmological constant (le aving the two brane tensions as free parameters) corresponding to a vanishi ng effective cosmological constant and a constant radion field. Taking thes e solutions as a background configuration, we perform a dimensional reducti on and study the effective theory in the case of one- and two-brane configu rations. We show that the radion field can have a positive mass squared, wh ich corresponds to a stabilization of the extra dimension, only for a repul sive nature of the Casimir force. This type of solution requires the presen ce of a negative tension brane. The solutions with one or two positive tens ion branes arising in this theory turn out to have negative radion mass squ ared, and therefore are not stable.