Gravitational forces in the Randall-Sundrum model with a scalar stabilizing field

We consider the problem of gravitational forces between point particles on the branes in a five-dimensional (5D) Randall-Sundrum model with two branes (at y1 and y2) and S1/Z2 symmetry of the fifth dimension. The matter on the branes is viewed as a perturbation on the vacuum metric and treated to linear order. In a previous work [R. Arnowitt and J. Dent, Phys. Rev. D 71, 124024 (2005).] it was seen that the trace of the transverse part of the 4D metric on the TeV brane, fT(y2), contributed a Newtonian potential enhanced by e2βy2 congruent with 1032 and thus produced gross disagreement with the experiment. In this work we include a scalar stabilizing field φ and solve the coupled Einstein and scalar equations to leading order for the case where φ02/M53 is small and the vacuum field φ0(y) is a decreasing function of y. fT then grows a mass factor e-μr where, however, μ is suppressed from its natural value, O(MPl), by an exponential factor e-(1+λb)βy2, λb>0. Thus agreement with the experiment depends on the interplay between the enhancing and decaying exponentials. Current data eliminates a significant part of the parameter space, and the Randall-Sundrum model will be sensitive to any improvements on the tests of the Newtonian force law at smaller distances. An example of coupling of the φ field to the Higgs field is examined and found to generally produce very small effects