  It has been speculated that the zero-point energy of the vacuum, regularized
due to the existence of a suitable ultraviolet cut-off scale, could be the
source of the non-vanishing cosmological constant that is driving the present
acceleration of the universe. We show that the presence of such a cut-off can
significantly alter the results for the Casimir force between parallel
conducting plates and even lead to repulsive Casimir force when the plate
separation is smaller than the cut-off scale length. Using the current
experimental data we rule out the possibility that the observed cosmological
constant arises from the zero-point energy which is made finite by a suitable
cut-off. Any such cut-off which is consistent with the observed Casimir effect
will lead to an energy density which is about 10^{12} times larger than the
observed one, if gravity couples to these modes. The implications are
discussed.
