Quantized bulk scalar fields in the Randall-Sundrum brane model

We examine the lowest order quantum corrections to the effective action arising from a quantized real scalar field in the Randall-Sundrum background spacetime. The leading term is the familiar vacuum, or Casimir, energy density. The next term represents an induced gravity term that can renormalize the 4-dimensional Newtonian gravitational constant. The calculations are performed for an arbitrary spacetime dimension. Two inequivalent boundary conditions, corresponding to twisted and untwisted field configurations, are considered. A careful discussion of the regularization and renormalization of the effective action is given, with the relevant counterterms found. It is shown that the requirement of self-consistency of the Randall-Sundrum solution is not simply a matter of minimizing the Casimir energy density. The massless, conformally coupled scalar field results are obtained as a special limiting case of our results. We clarify a number of differences with previous work.