Dark Matter in a Three-Brane Randall-Sundrum Scenario out of the Evanescent Limit

Abstract

The Nature of Dark Matter (DM), that constitutes approximately 25\% of the energy density in the Universe, is still eluding us. An intriguing possibility is that DM does indeed interacts with SM particles only gravitationally (the only mean by which we have detected it so far), albeit in an extra-dimensional scenario yet it has not been possible to detect it by some non-gravitational means. In a three-brane Randall-Sundrum setup, with DM located on a Deep Infra-Red GeV-TeV brane, and the SM on an Infra-Red TeV-PeV one, it was shown to be possible to recover the observed DM relic abundance and somewhat relax the hierarchy problem, whilst avoiding LHC stringent bounds on DM and KK graviton masses that constrain severely similar two-brane setups. The phenomenological results, however, have been obtained under the assumption that the bulk curvatures on the left ($k_1$) and the right ($k_2$) of the intermediate IR-brane are identical, $k_2 \to k_1$. Since the brane tension $\sigma_{\rm IR}$ of the intermediate brane is proportional to $k_2 - k_1$ and, therefore, vanishes, it is clear that this limit (for which the IR-brane becomes {\em evanescent}) is unphysical. We could say that this is {\em no brane}: if the brane tension of a brane vanishes, there is no brane in the bulk (pun intended). In this paper, therefore, we study in detail the theoretical framework needed to explore this interesting phenomenological possibility, {\em out of the evanescent brane limit}. We show that most of the formul\ae $\,$used in the {\em evanescent limit} are still valid for ${\cal O}(1)$ differences between $k_1$ and $k_2$ (thus, introducing no new unjustified hierarchy in the bulk). Once the relevant couplings of radions and KK gravitons are computed, we study the (enlarged) parameter space of the model looking for the region in which the relic DM abundance is recovered.