No Ghost State in the Brane World

TL;DR

This paper investigates the role of metric fluctuations in the Randall-Sundrum brane world scenario, demonstrating conditions under which ghost states are avoided and massless graviton propagation is preserved.

Contribution

It clarifies the gauge dependence of metric fluctuations and identifies conditions that eliminate ghost states in the spectrum.

Findings

Ghost states appear in massive modes without specific source relations.

Massless spin-2 propagation occurs without ghosts under certain source conditions.

The results align with the intermediate scale behavior of the GRS model.

Abstract

We discuss the role of the trace part of metric fluctuations $h_{MN}$ in the Randall-Sundrum scenario of gravity. Without the matter, this field ($h=\eta^{MN}h_{MN}$) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source $\tilde{T}_{MN}$, this field satisfies the linearized equation $\Box_4 h =16\pi G_5 T^{\mu}_{\mu}$. This may correspond to the scalar $\xi^5$ in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations ($h_{5\mu} =h_{55}=0$), one finds the source relation $\tilde{T}^{\mu}_{\mu}=2\tilde{T}_{55}$, which leads to the ghost states in the massive modes. In addition, if one requires $T_{44}=2(T_{22}+T_{33})$, it is found that in the limit of $m^2_h \to 0$ we have the massless spin-2 propagation without the ghost state. This exactly corresponds to the same situation as in the intermediate scales of Gregory-Rubakov-Sibiryakov (GRS) model.