We discuss a constraint on the scale \Lambda _ { NC } of noncommutative ( NC ) gauge field theory arising from consideration of the big bang nucleosynthesis ( BBN ) 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 vector-like 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 } \stackrel { > } { \sim } 3 TeV .
With a more stringent requirement , \Delta N _ { \nu } \lesssim 0.2 , the bound is considerably improved , \Lambda _ { NC } \stackrel { > } { \sim } 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 .