  Recently, there has been a certain amount of activity around the theme of
cosmological and astrophysical applications of noncommutative geometry models
of particle physics. We study space-time non-commutativity applied to the
hydrogen atom and the corrections induced to transitions frequencies. By
writing the Dirac equation for noncommutative Coulomb potential, we compute
noncommutative corrections of the energy levels using perturbation methods and
by comparing to the Lamb shift accuracy we get a bound on the parameter of
non-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 some
astrophysical and cosmological phenomena.
