Micro-orbits in a many-branes model and deviations from $1/r^2$ Newton's law

TL;DR

This paper explores how extra-dimensional brane models can cause deviations from Newton's inverse-square law in micro-orbits, proposing experimental tests to detect such deviations and potential dark matter implications.

Contribution

It introduces a method to analyze orbital deviations in a 5D brane-world model and suggests experimental setups to improve bounds on deviations from Newtonian gravity.

Findings

Orbits on distant branes differ significantly from Newtonian predictions.

The proposed experiments could improve current bounds on deviations by an order of magnitude.

The study provides a framework to detect extra-dimensional effects through orbital dynamics.

Abstract

We consider a 5-dimensional model with geometry ${\cal M} = {\cal M}_4 \times {\cal S}_1$, with compactification radius $R$. The Standard Model particles are localized onto a brane located at y=0, with identical branes localized at different points in the extra dimension. Objects located on our brane can orbit around objects located on a brane at a distance $d=y/R$, with an orbit and a period significantly different from the standard Newtonian ones. We study the kinematical properties of the orbits, finding that it is possible to distinguish one motion from the other in a large region of the initial conditions parameter space. This is a warm-up to study if a SM-like mass distribution on one (or more) distant brane(s) may represent a possible dark matter candidate. After using the same technique to the study of orbits of objects lying on the same brane ($d=0$), we apply this method to detect generic deviations from the inverse-square Newton's law. We propose a possible experimental setup to look for departures from Newtonian motion in the micro-world, finding that an order of magnitude improvement on present bounds can be attained at the 95% CL under reasonable assumptions.