Abstract
The problem of the Majorana neutrino mass generated in the Arkani-Hamed--Dimopoulos--Dvali model with n extra spatial dimensions is discussed. Taking into account constraints on the neutrino masses coming from cosmological observations, it is possible to obtain lower limits on the size of the extra dimensions as large as ${10}^{\ensuremath{-}6}\mathrm{mm}.$ In the case of $n=4$ it is easy to lower the fundamental scale of gravity from the Planck energy to the electroweak scale $\ensuremath{\sim}1\mathrm{TeV}$ without imposing any additional constraints. A link between the half-life of neutrinoless double beta decay and the size of extra dimensions is discussed.
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