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 ${\rho }_1\lesssim 100\mathrm{GeV}\ll {\rho }_T$. The Standard Model (SM) 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 ${\rho }_1\lesssim 3\mathrm{GeV}$, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational wave background at the nanohertz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for $0.15\lesssim m_{\chi }\lesssim 2\mathrm{GeV}$ the relic abundance is reproduced and all constraints are satisfied.