Testing extra dimensions with boundaries using Newton's law modifications

TL;DR

This paper investigates how extra-dimensional spaces with boundaries, under various boundary conditions, can modify Newton's law, and identifies which models are consistent with Yukawa-type deviations.

Contribution

It analyzes the impact of boundary conditions on extra-dimensional models and determines which configurations can produce consistent Newton's law modifications.

Findings

Certain extra-dimensional models with boundaries are incompatible with Yukawa-type Newton's law modifications.

Disk and interval geometries impose specific constraints on boundary conditions for consistent modifications.

Some previously used models in the literature are ruled out based on these boundary condition analyses.

Abstract

Extra dimensions with boundaries are often used in the literature, to provide phenomenological models that mimic the standard model. In this context, we explore possible modifications to Newton's law due to the existence of an extra-dimensional space, at the boundary of which the gravitational field obeys Dirichlet, Neumann or mixed boundary conditions. We focus on two types of extra space, namely, the disk and the interval. As we prove, in order to have a consistent Newton's law modification (i.e., of the Yukawa-type), some of the extra-dimensional spaces that have been used in the literature, must be ruled out.