Extra Dimensions are Dark: I.

Extra dimensions (ED) can provide a useful tool for model-building. In this paper we introduce a single, flat ED extension of the kinetic-mixing/dark photon (DP) portal for dark matter (DM) interactions with the Standard Model (SM) assuming a compactification `radius' of order $R^{-1}\sim10-1000$ MeV and examine the resulting modifications to and augmentation of the usual DP phenomenology. In the present scenario, both the DP and DM experience the full 5-D while the SM fields are constrained to lie on a 4-D brane at the boundary of the ED. Such a setup can naturally yield the observed value of the DM relic density and explain the required rough degeneracy of the DM and DP masses needed to obtain it. Gauge symmetry breaking can occur via boundary conditions without the introduction of an additional singlet Higgs scalar thus avoiding all constraints associated with the coupling of such a field to the usual SM Higgs field in 5-D. The self-consistency of the field redefinitions that map the gauge fields into a canonical basis and thus removing the kinetic mixing terms is found to lead to a strong model building constraint on the ED setup involving a brane localized kinetic term for the 5-D gauge field on the SM brane. Multiple variations of this scenario are found to be possible which are consistent with all current experimental constraints but which predict very different phenomenologies. In this paper, after setting up the general model formalism, we discuss in detail the case of a complex scalar 5-D DM field, consistent with constraints arising from the CMB, which may or may not obtain a vacuum expectation value (vev). The resulting Kaluza-Klein (KK) towers of both the DM and DP fields are found to yield interesting and distinctive signatures.