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Recently, there has been a certain amount of activity around the theme ofcosmological and astrophysical applications of noncommutative geometry modelsof particle physics. We study space-time non-commutativity applied to thehydrogen atom and the corrections induced to transitions frequencies. Bywriting the Dirac equation for noncommutative Coulomb potential, we computenoncommutative corrections of the energy levels using perturbation methods andby comparing to the Lamb shift accuracy we get a bound on the parameter ofnon-commutativity. We use this bound to study the effects on the Lyman-{\alpha}ray and by induction look the possible influence of non-commutativity on someastrophysical and cosmological phenomena.

Lyman-Alpha Spectroscopy in Non-Commutative Space-Time