The Casimir Force in Randall Sundrum Models with q+1 dimensions

We evaluate the Casimir force between two parallel plates in Randall Sundrum (RS) scenarios extended by q compact dimensions. After giving exact expressions for one extra compact dimension (RS 6D model), we generalize to an arbitrary number of compact dimensions. We present the complete calculation for both two brane scenario (RSI model) and one brane scenario (RSII models) using the method of summing over the modes. We investigate the effects of extra dimensions on the magnitude and sign of the force, and comment on limits for the size and number of the extra dimensions.