Brane localization of gravity in higher derivative theory

TL;DR

This paper investigates how higher derivative Euler density corrections in gravity theories affect the localization of gravity on domain walls, demonstrating the existence of a massless graviton and a continuum of massive modes.

Contribution

It explicitly solves the linearized gravity equations around domain wall solutions in higher derivative gravity, confirming graviton localization and the spectrum of fluctuations.

Findings

Existence of a localized massless graviton on the domain wall

Presence of a continuous spectrum of massive bulk modes

Higher derivative corrections do not prevent gravity localization

Abstract

We consider a class of higher order corrections in the form of Euler densities of arbitrary rank $n$ to the standard gravity action in $D$ dimensions. We have previously shown that this class of corrections allows for domain wall solutions despite the presence of higher powers of the curvature. In the present paper we explicitly solve the linearized equation of motion for gravity fluctuations around the domain wall background and show that there always exist one massless state (graviton) propagating on the wall and a continuous tower of massive states propagating in the bulk.