Near Threshold Kaluza-Klein Graviton Decays and the Dark Dimension

Near threshold, intra-tower decays of Kaluza-Klein (KK) gravitons are pure $d$-wave, with rate $\mathrm{\Gamma }\propto p^5$ in the decay products momentum $p$, rather than the $s$-wave $\mathrm{\Gamma }\propto p$ assumed in the dark dimension literature. In a flat dark dimension this excludes KK gravitons as a dark matter candidate. Even if some other source of dark matter is assumed, the irreducible freeze-in abundance of KK gravitons produce MeV gamma rays which allows one to set upper limits on the reheating temperature; additionally using the lower bound on the reheating temperature from big-bang nucleosynthesis and the cosmic microwave background requires the radius of the extra dimension to be almost three orders of magnitude smaller than the distance conjecture would naively prefer, $R\sim {\mathrm{\Lambda }}^{-1\mathrm{/}4}$.