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We construct an explicit model of the gravity trapping domain-wall potential, where for the first time we can study explicitly the graviton wave function fluctuations for any thickness of domain wall. A concrete form of the potential depends on one parameter 0 ≤ x ≤ π/2 , which effectively parameterizes the thickness of the domain wall with specific limits x → 0 and x → π/2 2 corresponding to the thin and the thick wall, respectively. The analysis of continuum Kaluza-Klein fluctuations yields explicit expressions for both 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 behavior, and which could sizably affect the modifications of the four-dimensional Newton’s law at distances that typically are by 4 orders of magnitude larger than those relevant for Newton’s law modifications of thin walls.
Date Posted: 25 January 2011
This document has been peer reviewed.