  In this paper, the generation of topological energy in models with large
extra dimensions is investigated. The origin of this energy is attributed to a
topological deformation of the standard Minkowski vacuum due to
compactification of extra dimensions. This deformation is seen to give rise to
an effective, finite energy density due to massive Kaluza-Klein modes of
gravitation. It's renormalized value is seen to depend on the size of the extra
dimensions instead of the UV cut-off of the theory. It is shown that if this
energy density is to contribute to the observed cosmological constant, there
will be extremely stringent bounds on the number of extra dimensions and their
size.
