  In models of universal extra dimensions, gravity and all standard model
fields propagate in the extra dimensions. Previous studies of such models have
concentrated on the Kaluza-Klein (KK) partners of standard model particles.
Here we determine the properties of the KK gravitons and explore their
cosmological implications. We find the lifetimes of decays to KK gravitons, of
relevance for the viability of KK gravitons as dark matter. We then discuss the
primordial production of KK gravitons after reheating. The existence of a tower
of KK graviton states makes such production extremely efficient: for reheat
temperature T_RH and d extra dimensions, the energy density stored in gravitons
scales as T_RH^{2+3d/2}. Overclosure and Big Bang nucleosynthesis therefore
stringently constrain T_RH in all universal extra dimension scenarios. At the
same time, there is a window of reheat temperatures low enough to avoid these
constraints and high enough to generate the desired thermal relic density for
KK WIMP and superWIMP dark matter.
