Radion on the de Sitter brane

TL;DR

This paper investigates the behavior of the radion field in de Sitter brane models, revealing its absence in single-brane scenarios and its negative mass-squared in two-brane setups, with implications for brane-world cosmology.

Contribution

It provides a covariant curvature tensor formalism analysis of the radion on de Sitter branes, clarifying its spectrum and mass properties, and relates it to brane displacement in the metric approach.

Findings

No radion in single de Sitter brane with positive tension.

Radion has negative mass-squared in two-brane models.

Radion corresponds to brane displacement and affects scalar perturbations.

Abstract

The radion on the de Sitter brane is investigated at the linear perturbation level, using the covariant curvature tensor formalism developed by Shiromizu, Maeda and Sasaki. It is found that if there is only one de Sitter brane with positive tension, there is no radion and thus the ordinary Einstein gravity is recoverd on the brane other than corrections due to the massive Kaluza-Klein modes. As a by-product of using the covariant curvature tensor formalism, it is immediately seen that the cosmological scalar, vector and tensor type perturbations all have the same Kaluza-Klein spectrum. On the other hand, if there are two branes with positive and negative tensions, the gravity on each brane takes corrections from the radion mode in addition to the Kaluza-Klein modes and the radion is found to have a negative mass-squared proportional to the curvature of the de Sitter brane, in contrast to the flat brane case in which the radion mass vanishes and degenerates with the 4-dimensional graviton modes. To relate our result with the metric perturbation approach, we derive the second order action for the brane displacement. We find that the radion identified in our approach indeed corresponds to the relative displacement of the branes in the Randall-Sundrum gauge and describes the scalar curvature perturbations of the branes in the gaussian normal coordinates around the branes. Implications to the inflationary brane universe are briefly discussed.