Limits to gauge coupling in the dark sector set by the non-observation
  of instanton-induced decay of Super-Heavy Dark Matter in the Pierre Auger
  Observatory data
  We investigate instanton-induced decay processes of super-heavy dark matter
particles $X$ produced during the inflationary epoch. Using data collected at
the Pierre Auger Observatory we derive a bound on the reduced coupling constant
of gauge interactions in the dark sector: $\alpha_X^{\rm eff} \lesssim 0.09$,
for $10^{10} < M_X/{\rm GeV} < 10^{16}$. We show that this upper limit on
$\alpha_X^{\rm eff}$ is complementary to that obtained from the non-observation
of tensor modes in the cosmic microwave background.
