Brane gravity , massless bulk scalar and self - tuning solution of the cosmological constant problem

We show that a self-tuning mechanism of the cosmological constant could work in 5D non-compact space with Z 2 symmetry with scalar kinetic energy term. The standard model matter fields live only on the 4 dimensional (4D) brane. The change of vacuum energy on the brane (brane cosmological constant) by, for instance, electroweak and QCD phase transitions, just gives rise to dynamical shifts of the profiles of the background metric and scalar fields in the extra dimension, keeping 4D space-time flat without any fine-tuning. To avoid naked singularities in the bulk, the brane cosmological constant should be negative. We introduce an additional brane-localized 4D Einstein-Hilbert term so as to provide the observed 4D gravity with the non-compact extra dimension. Without assuming a large hierarchy between 5D and 4D gravity scales, the − 1 r Newtonian potential successfully arise in some parameter range. We show this phenomenon explicitly for the case of vanishing bulk cosmological constant.