Inferring type and scale of noncommutativity from the PTOLEMY experiment

If neutrinos are Dirac particles and their right-handed component can be copiously produced in the early universe, then they could influence a direct observation of the cosmic neutrino background, which, most likely, will come about with the recently proposed PTOLEMY experiment. For the production mechanism of right-handed neutrinos we use a state-of-the-art version of gauge field theory deformed by the spacetime noncommutativity, to disclose by it not only the decoupling temperature for the said neutrino component, but also the otherwise hidden coupling temperature. Considering two relevant processes, the plasmon decay and the neutrino elastic scattering, we study the interplay between the structure of the noncommutativity parameter $\theta^{\mu \nu}$ (type of noncommutativity) and the reheating temperature after inflation to obtain otherwise elusive upper bound on the scale of noncommutativity $\Lambda_{\rm NC}$. If PTOLEMY enhanced capture rate is due to spacetime noncommutativity, we verify that a nontrivial maximum upper bound on $\Lambda_{\rm NC}$ (a way below the Planck scale) emerges for a space-like $\theta^{\mu \nu}$ and sufficiently high reheating temperature.