Constraining spacetime noncommutativity with primordial nucleosynthesis

We discuss a constraint on the scale ${\Lambda }_{\mathrm{NC}}$ 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 ${\Lambda }_{\mathrm{NC}}\gtrsim 3\mathrm{TeV}$. With a more stringent requirement, $\Delta N_{\nu }\lesssim 0.2$, the bound is considerably improved, ${\Lambda }_{\mathrm{NC}}\gtrsim {10}^3\mathrm{TeV}$. 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.