Linearized gravity on the Randall-Sundrum two-brane background with curvature terms in the action for the branes

TL;DR

This paper investigates gravitational perturbations in a modified Randall-Sundrum two-brane model with curvature terms, revealing conditions for tachyonic modes and ghost-like massive modes depending on the bulk and brane gravitational constants.

Contribution

It introduces a generic method to identify tachyonic modes in the model and analyzes their existence under various parameter conditions, including negative bulk gravitational constant.

Findings

Tachyonic modes may exist only if the bulk gravitational constant is negative.

Massive gravitational modes can be ghost-like when the bulk constant is negative.

The massless mode remains non-ghost if tachyons are absent.

Abstract

We study gravitational perturbations in the Randall-Sundrum two-brane background with scalar-curvature terms in the action for the branes, allowing for positive as well as negative bulk gravitational constant. In the zero-mode approximation, we derive the linearized gravitational equations, which have the same form as in the original Randall-Sundrum model but with different expressions for the effective physical constants. We develop a generic method for finding tachyonic modes in the theory, which, in the model under consideration, may exist only if the bulk gravitational constant is negative. In this case, if both brane gravitational constants are nonzero, the theory contains one or two tachyonic mass eigenvalues in the gravitational sector. If one of the brane gravitational constants is set to zero, then either a single tachyonic mass eigenvalue is present or tachyonic modes are totally absent depending on the relation between the nonzero brane gravitational constant and brane separation. In the case of negative bulk gravitational constant, the massive gravitational modes have ghost-like character, while the massless gravitational mode is not a ghost in the case where tachyons are absent.