Steadiness of Stabilized Randall–Sundrum Model with Respect to Quantum Corrections

In the Randall–Sundrum model stabilized with the help of the Goldberger–Wise scalar field, the lowest order vacuum quantum corrections to the energy-momentum tensor of the scalar and tensor fields are considered. It is shown that the corresponding vacuum energy density of the fields in the bulk leads to the Casimir effect. Using the dimensional regularization method and the Abel–Plana formula, the divergences have been isolated and the vacuum energy density has been renormalized. An analytical expression for the Casimir force is obtained and an estimate of its influence on the model parameters is made. It has been found that the quantum corrections lead only to a negligibly small decrease in the distance between the branes, i.e. the model possesses steadiness with respect to quantum corrections.