Modified Einstein equation of dilatonic braneworld model with nonminimal derivative coupling in the bulk

This study is an analytical study to determine modified Einstein equation. The model used in this study is the dilatonic Braneworld 4+n dimensions which is embedded into the bulk 5+n dimensions and the addition of nonminimal derivative coupling term in the bulk. The determination of the modified Einstein equation is carried out using the gradient expansion method. The gradient expansion method is carried out by taking the low energy limit in which the brane tension is greater than the energy density of the matter. Next, the field equation is solved by some order of perturbation. From this method, we get the Field equation which modify Einstein equations in the general relativity theory by addition extra terms. The extra term is expected to act as a source of dark energy.