Dark Branes for Dark Matter

We propose a setup for the origin of dark matter based on spacetime with a warped extra dimension and three branes: the Planck brane, the TeV brane, at a (few) TeV scale $\rho_T$, and a dark brane, at a (sub)-GeV scale $\rho_1\lesssim 100$ GeV $\ll\rho_T$. The Standard Model is localized in the TeV brane, thus solving the Higgs hierarchy problem, while the dark matter $\chi$, a Dirac fermion with mass $m_\chi<\rho_1$, is localized in the dark brane. The radion, with mass $m_r<m_\chi$, interacts strongly ($\sim m_\chi/\rho_1\sim\mathcal O(1)$) with dark matter and very weakly ($\sim m_{f}\rho_1/\rho_T^2\ll 1$) with the Standard Model matter $f$. The generic conflict between the bounds on its detection signatures and its proper relic abundance is avoided as dark matter annihilation is $p$-wave suppressed. The former is determined by its very weak interactions with the SM and the latter by its much stronger annihilation into radions. Therefore, there is a vast range in the Dark Matter's parameter space where the correct relic abundance is achieved consistently with the existing bounds. Moreover, for the dark brane with $\rho_1\lesssim 3$ GeV, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational waves background at the nanoHz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for $0.15 \textrm{ GeV}\lesssim m_\chi\lesssim 2$ GeV the relic abundance is reproduced and all constraints are satisfied.