Gravity Trapping on a Finite Thickness Domain Wall: An Analytic Study

TL;DR

This paper presents an explicit analytic model of gravity trapping on a finite thickness domain wall, analyzing graviton fluctuations and resonance effects that influence Newton's law at large distances.

Contribution

It provides the first explicit analytic study of graviton wave functions for any domain wall thickness, including resonance behavior and its impact on gravity modifications.

Findings

Explicit expressions for Kaluza-Klein fluctuations

Resonance conditions for thick walls

Potential impact on Newton's law at large scales

Abstract

We construct an explicit model of gravity trapping domain wall potential where for the first time we can study explicitly the graviton wave function fluctuations for any thickness of the domain wall. A concrete form of the potential depends on one parameter 0 <= x <= pi/2, which effectively parameterizes the thickness of the domain wall with specific limits x -> 0 and x -> pi/2 corresponding to the thin and the thick wall, respectively. The analysis of the continuum Kaluza Klein fluctuations yields explicit expressions for both the small and large Kaluza Klein energy. We also derive specific explicit conditions in the regime x > 1, for which the fluctuation modes exhibit a resonance behaviour, and which could sizably affect the modifications of the four-dimensional Newton's law at distances, which typically are by four orders of magnitude larger than those relevant for Newton's law modifications of thin walls.