The Casimir force in noncommutative Randall-Sundrum models

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.