Abstract
The Randall-Sundrum model with a small curvature is considered in which five-dimensional Planck scale lies in the TeV region. The cross sections for interactions of ultra-high energy cosmic neutrinos with nucleons are calculated. It is shown that effects related with Kaluza-Klein graviton excitations can be detected in deeply penetrating inclined air showers induced by these neutrinos. The expected number of the inclined air showers at the Auger Observatory is estimated as a function of two parameters of the model. 1. WARPED EXTRA DIMENSION WITH THE SMALL CURVATURE One of the most important problems of the modern particle physics is the hierarchy problem, i.e. unnaturally large ratio of the gravity scale (10 19
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