Precise calculation of the relic density of Kaluza-Klein dark matter in universal extra dimensions

We revisit the calculation of the relic density of the lightest Kaluza-Klein particle (LKP) in the model of Universal Extra Dimensions. The Kaluza-Klein (KK) particle spectrum at level one is rather degenerate, and various coannihilation processes may be relevant. We extend the calculation of hep-ph/0206071 to include coannihilation processes with all level one KK particles. In our computation we consider a most general KK particle spectrum, without any simplifying assumptions. In particular, we do not assume a completely degenerate KK spectrum and instead retain the dependence on each individual KK mass. As an application of our results, we calculate the Kaluza-Klein relic density in the Minimal UED model, turning on coannihilations with all level one KK particles. We then go beyond the minimal model and discuss the size of the coannihilation effects separately for each class of level 1 KK particles. Our results provide the basis for consistent relic density computations in arbitrarily general models with Universal Extra Dimenions.