Constraining spacetime noncommutativity with primordial nucleosynthesis

TL;DR

This paper constrains the noncommutative scale in gauge theories using primordial nucleosynthesis data, establishing bounds of over 3 TeV and up to 1000 TeV based on neutrino contributions to early universe energy density.

Contribution

It provides the first cosmological bounds on the noncommutative scale from big bang nucleosynthesis considering right-handed neutrino interactions.

Findings

Bound on noncommutative scale > 3 TeV for ΔN_ν=1

Stricter bound > 1000 TeV for ΔN_ν<0.2

Decoupling temperature remains below the noncommutative scale

Abstract

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.