Exploring extra dimensions with scalar waves

TL;DR

This paper introduces the physics of extra dimensions through scalar wave analysis in ADD, Randall-Sundrum, and DGP models, highlighting how scalar fields behave differently at various scales and implications for gravity and experiments.

Contribution

It provides a pedagogical analysis of scalar wave propagation in three key extra-dimensional models, including explicit calculations of scalar fields from point sources.

Findings

Scalar fields behave as four-dimensional at large distances in ADD and Randall-Sundrum models.

In the DGP model, scalar fields exhibit higher-dimensional behavior at long distances.

Insights into gravity's weakness and experimental implications are discussed.

Abstract

This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be confined to a four dimensional space-time called the brane; the brane is a slice through a higher dimensional space-time called the bulk. The geometry of the ADD, Randall-Sundrum and DGP space-times is described and the relation between Randall-Sundrum and Anti-de-Sitter space-time is explained. The necessary differential geometry background is introduced in an appendix that presumes no greater mathematical preparation than multivariable calculus. The ordinary wave equation and the Klein-Gordon equation are briefly reviewed followed by an analysis of the propagation of scalar waves in the bulk in all three extra-dimensional models. We also calculate the scalar field produced by a static point source located on the brane for all three models. For the ADD and Randall-Sundrum models at large distances the field looks like that of a point source in four space-time dimensions but at short distances it crosses over to a form appropriate to the higher dimensional space-time. For the DGP model the field has the higher dimensional form at long distances rather than short. The scalar field results provide qualitative insights into the corresponding behavior of gravitational fields. In particular the explanation within the ADD and Randall-Sundrum model of the weakness of gravity compared to other forces is discussed as are the implications of the two models for colliders and other experiments.