Self-tuning of the cosmological constant and Einstein Gravity on the brane

We show that a self-tuning mechanism of the cosmological constant could work in 5D non-compact space-time. The standard model matter fields live only on the 4D brane. The change of vacuum energy on the brane just gives rise to dynamical shifts of the profiles of the background metric and a bulk scalar field in the extra dimension, keeping 4D space-time flat. To obtain the Newtonian potential on the brane, we introduce an additional brane-localized 4D Einstein-Hilbert term.