Steadiness of Stabilized Randall–Sundrum Model with Respect to Casimir Effect

The paper considers the Casimir effect in the stabilized Randall–Sundrum model, which arises due to the propagation of the gravitational field and the Goldberger–Wise scalar field in the five-dimensional bulk between two branes. The Casimir energy density of the scalar modes is calculated analytically. Using the dimensional regularization method and writing the regularized energy density as the Hurwitz zeta function, divergences are identified and the Casimir energy density of the scalar modes is renormalized. Similar estimates are made for the Casimir energy density of tensor modes. An estimate of the Casimir effect is made considering all the modes on the equations and parameters of the model. It is found that such quantum corrections do not change the form of the solution of the equations of motion of the model and lead only to a negligible decrease in the background scalar field on the Planck brane and the distance between the branes; i.e., the model is stable with respect to the Casimir effect.