Constraining spacetime noncommutativity with primordial nucleosynthesis
  We discuss a constraint on the scale $\Lambda_{\rm NC}$ 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 $\Lambda_{\rm NC} \stackrel{>}{\sim}$ 3
TeV. With a more stringent requirement, $\Delta N_\nu \lesssim 0.2$, the bound
is considerably improved, $\Lambda_{\rm NC} \stackrel{>}{\sim} 10^3$ 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.
