Surface Casimir densities and induced cosmological constant on parallel branes in AdS

TL;DR

This paper calculates the vacuum-induced surface energies and cosmological constant on parallel branes in AdS space, showing how these effects depend on boundary conditions and separation, with implications for the cosmological constant problem.

Contribution

It provides a detailed analysis of surface energy-momentum tensors for scalar fields with Robin boundary conditions on branes in AdS, including the effects of different boundary parameters and brane separations.

Findings

Surface energies are finite for separated branes in odd dimensions.

Induced surface densities lead to an exponentially suppressed cosmological constant at large brane separations.

The model's predictions align with observed cosmological constant values in the Randall-Sundrum scenario.

Abstract

Vacuum expectation value of the surface energy-momentum tensor is evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel branes located on (D+1)-dimensional AdS bulk. The general case of different Robin coefficients on separate branes is considered. As an regularization procedure the generalized zeta function technique is used, in combination with contour integral representations. The surface energies on the branes are presented in the form of the sums of single brane and second brane-induced parts. For the geometry of a single brane both regions, on the left (L-region) and on the right (R-region), of the brane are considered. The surface densities for separate L- and R-regions contain pole and finite contributions. For an infinitely thin brane taking these regions together, in odd spatial dimensions the pole parts cancel and the total surface energy is finite. The parts in the surface densities generated by the presence of the second brane are finite for all nonzero values of the interbrane separation. It is shown that for large distances between the branes the induced surface densities give rise to an exponentially suppressed cosmological constant on the brane. In the Randall-Sundrum braneworld model, for the interbrane distances solving the hierarchy problem between the gravitational and electroweak mass scales, the cosmological constant generated on the visible brane is of the right order of magnitude with the value suggested by the cosmological observations.