  Using a fully-fledged formulation of gauge field theory deformed by the
spacetime noncommutativity, we study its impact on relic neutrino direct
detection, as proposed recently by the PTOLEMY experiment. The noncommutative
background tends to influence the propagating neutrinos by providing them with
a tree-level vector-like coupling to photons, enabling thus otherwise
right-handed (RH) neutrinos to be thermally produced in the early universe.
Such a new component in the universe's background radiation has been switched
today to the almost fully active sea of non-relativistic neutrinos, exerting
consequently some impact on the capture on tritium at PTOLEMY. The
peculiarities of our nonperturbative approach tend to reflect in the cosmology
as well, upon the appearances of the coupling temperature, above which
  RH neutrinos stay permanently decoupled from thermal environment. This
entails the maximal scale of noncommutativity as well, being of order of
$10^{-4} M_{Pl}$, above which there is no impact whatsoever on the capture
rates at PTOLEMY. The latter represents an exceptional upper bound on the scale
of noncommutativity coming from phenomenology.
