Bound on a diffuse flux of ultra-high energy neutrinos in the ADD model

The search for ultra-high energy downward-going and Earth-skimming cosmic neutrinos by the Surface Detector array of the Pierre Auger Observatory (PAO) is analyzed in the ADD model with n extra flat spatial dimensions. We assumed that the diffuse neutrino flux dN_nu/dE_nu$ is equal to k E_nu^(-20) in the energy range 10^(17) eV - 2.5 10^(19) eV. Taking into account that no neutrino events where found by the PAO, we have estimated an upper bound on a value of k. It is shown that this bound can be stronger than the upper bound on k recently obtained by the Pierre Auger Collaboration, depending on n and (n+4)-dimensional gravity scale M_D.