We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero point energy of the vacuum .
We derive the Casimir force between parallel conducting plates as a function of the following scales : plate separation , radius of the extra dimension and cutoff energy scale .
We find that there are critical values of these scales where the Casimir force between the plates changes sign .
For the cutoff energy scale required to reproduce the observed value of the cosmological constant , we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation d _ { 0 } = 0.6 mm , assuming a zero radius of the extra dimension ( no extra dimension ) .
This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of 100 nm .
For a non-zero extra dimension radius , the critical separation d _ { 0 } gets even larger than 0.6 mm and remains inconsistent with Casimir force experiments .
We conclude that with or without the presence of a compact extra dimension , vacuum energy with any suitable cutoff can not play the role of the cosmological constant .