NMC and the Fine-Tuning Problem on the Brane

We propose a new solution to the fine-tuning problem related to coupling constant of the potential. We study a quartic potential of the form in the framework of the Randall-Sundrum type II braneworld model in the presence of a Higgs field which interacts nonminimally with gravity via a possible interaction term of the form . Using the conformal transformation techniques, the slow-roll parameters in high energy limit are reformulated in the case of a nonminimally coupled scalar field. We show that, for some value of a coupling parameter and brane tension , we can eliminate the fine-tuning problem. Finally, we present graphically the solutions of several values of the free parameters of the model.