Quantum Radion on de Sitter branes

TL;DR

This paper investigates the quantum fluctuations of the radion field between de Sitter branes in an anti-de Sitter bulk, analyzing its effects on brane cosmology and stability without requiring stabilization mechanisms.

Contribution

It derives the effective action for the quantum radion and evaluates its impact on brane energy density, revealing small effects despite radion instability.

Findings

Quantum radion contributes minimally to brane energy density.

Radion remains unstable with negative mass squared but has limited physical impact.

No stabilization mechanism needed for small quantum effects.

Abstract

The quantum fluctuation of the relative location of two (n-1)-dimensional de Sitter branes (i.e., of n spacetime dimensions) embedded in the (n+1)-dimensional anti-de Sitter bulk, which we shall call the quantum radion, is investigated at the linear perturbation level. The quantization of the radion is done by deriving the effective action of the radion. Assuming the positive tension brane is our universe, the effect of the quantum radion is evaluated by using the effective Einstein equations on the brane in which the radion contributes to the effective energy momentum tensor at the linear order of the radion amplitude. Specifically, the rms effective energy density arising from the quantum radion is compared with the background energy density. It is found out that this ratio remains small for reasonable values of the parameters of the model even without introducing a stabilizing mechanism for radion, although the radion itself has a negative mass squared and is unstable. The reason behind this phenomenon is also discussed.