Contribution of Kaluza-Klein modes to vacuum energy in models with large extra dimensions $&$ the Cosmological constant

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.