Constraining spacetime noncommutativity with primordial nucleosynthesis

We discuss a constraint on the scale Lambda(NC) of noncommutative (NC) gauge field theory arising from consideration of the big bang nucleosynthesis of light elements. The propagation of neutrinos in the NC background described by an antisymmetric tensor theta(mu nu) does result in a tree-level vectorlike coupling to photons in a generation-independent manner, raising thus a possibility to have an appreciable contribution of three light right-handed (RH) fields to the energy density of the Universe at nucleosynthesis time. Considering elastic scattering processes of the RH neutrinos off charged plasma constituents at a given cosmological epoch, we obtain for a conservative limit on an effective number of additional doublet neutrinos Delta N-nu=1, a bound Lambda(NC)greater than or similar to 3 TeV. With a more stringent requirement, Delta N-nu less than or similar to 0.2, the bound is considerably improved, Lambda(NC)greater than or similar to 10(3) TeV. For our bounds the theta expansion of the NC action stays always meaningful, since the decoupling temperature of the RH species is perseveringly much less than the inferred bound for the scale of noncommutativity.