The Casimir force in noncommutative Randall-Sundrum models

TL;DR

This study investigates how spacetime noncommutativity influences the Casimir force in Randall-Sundrum models, deriving bounds on noncommutative scales and interbrane distances based on experimental data.

Contribution

It introduces the effect of spacetime noncommutativity into Randall-Sundrum models and constrains the noncommutative scale using Casimir force measurements.

Findings

Noncommutative scale cutoff is bounded around 10^3 TeV.

Interbrane distance estimates are approximately 20.5 and 18.4 for different parameters.

Noncommutativity affects Casimir force at small plate separations.

Abstract

In this paper we study the effect of spacetime noncommutativity in the 5-dimensional Randall-Sundrum brane worlds on the Casimir force acting on a pair of parallel plates. We show that the presence of a noncommutative scale length affects the nature of the Casimir force for small plate separation. Using accurate experimental bounds for the Casimir force in parallel plate geometry, we find an upper bound for the noncommutative cutoff of the order of $10^{3}$ TeV, and that the size of the interbrane distance in RSI model is approximately given by $kR\lesssim20.5$ and $kR\lesssim18.4$ for $k=10^{19}$ GeV and $k=10^{16}$GeV, respectively.