Dark matter in UED : the role of the second KK level

We perform a complete calculation of the relic abundance of the KK-photon LKP in the universal extra dimension model including all coannihilation channels and all resonances. We show that the production of level 2 particles which decay dominantly into SM particles contribute significantly to coannihilation processes involving level 1 KK-leptons. As a result the preferred dark matter scale is increased to $R^{-1}=1.3$~TeV. A dark matter candidate at or below the TeV scale can only be found in the non-minimal model by reducing the mass splittings between the KK-particles and the LKP. The LKP nucleon scattering cross section is typically small, $\sigma < 10^{-10}$~pb, unless the KK-quarks are nearly degenerate with the LKP.