Quantum Fluctuations for de Sitter Branes in Bulk AdS(5)

TL;DR

This paper investigates quantum scalar field fluctuations in a de Sitter brane setup within an anti-de Sitter bulk, revealing divergence issues near the branes and the behavior of Kaluza-Klein modes.

Contribution

It introduces a dimensional reduction approach to analyze quantum fluctuations on de Sitter branes in AdS space, addressing divergence problems and mode spectrum behavior.

Findings

Surface divergences occur near the branes but can be eliminated by constraining the field.

The ratio of Kaluza-Klein to lowest mode fluctuations vanishes as one brane moves to infinity.

Quantum fluctuations depend on the boundary conditions and field couplings.

Abstract

The vacuum expectation value of the square of the field fluctuations of a scalar field on a background consisting of {\it two} de Sitter branes embedded in an anti-de Sitter bulk are considered. We apply a dimensional reduction to obtain an effective lower dimensional de Sitter space equation of motion with associated Kaluza-Klein masses and canonical commutation relations. The case of a scalar field obeying a restricted class of mass and curvature couplings, including massless, conformal coupling as a special case, is considered. We find that the local behaviour of the quantum fluctuations suffers from surface divergences as we approach the brane, however, if the field is {\it constrained} to its value on the brane from the beginning then surface divergences disappear. The ratio of $<\phi^2>$ between the Kaluza-Klein spectrum and the lowest eigenvalue mode is found to vanish in the limit that one of the branes goes to infinity.