Relaxing Cosmological Constraints on Large Extra Dimensions
  We reconsider cosmological constraints on extra dimension theories from the excess production of Kaluza-Klein gravitons. We point out that, if the normalcy temperature is above 1 GeV, then graviton states produced at this temperature will decay early enough that they do not affect the present day dark matter density, or the diffuse gamma ray background. We rederive the relevant cosmological constraints for this scenario. 
Cosmin Macesanu, Mark Trodden