Cosmological Constraints on Dark Neutrino Towers

We reexamine a dynamical dark matter model with Kaluza-Klein (KK) towers of gravitons and neutrinos fitting together in the dark dimension. We show that even though gravitational decays of neutrino KK towers have little impact in cosmology the weak decay channel could have significant cosmological effects. Taking conservative upper bounds on the dark matter decay rate into two photons before recombination and on the number of effective extra neutrino species $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ we derive constraints on the conversion rate from active to sterile species despite the dependence of the mixing angle on the KK mode mass. We also provide counterarguments to a recent claim suggesting that the bounds on $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ rule out micron-sized extra dimensions.