Cosmological implications of photon-flux upper limits at ultra-high energies in scenarios of Planckian-interacting massive particles for dark matter

Abstract

We present a thorough search for signatures that would be suggestive of super-heavy $X$ particles decaying in the Galactic halo, in the data of the Pierre Auger Observatory. From the lack of signal, we derive upper limits for different energy thresholds above ${\gtrsim}10^8$ GeV on the expected secondary by-product fluxes from $X$-particle decay. Assuming that the energy density of these super-heavy particles matches that of dark matter observed today, we translate the upper bounds on the particle fluxes into tight constraints on the couplings governing the decay process as a function of the particle mass. We show that instanton-induced decay processes allow us to derive a bound on the reduced coupling constant of gauge interactions in the dark sector: \alpha_X \alt 0.09, for 10^{9} \alt M_X/\text{GeV} < 10^{19}. This upper limit on $\alpha_X$ is complementary to the non-observation of tensor modes in the cosmic microwave background in the context of Planckian-interacting massive particles for dark matter produced during the reheating epoch. Viable regions for this scenario to explain dark matter are delineated in several planes of the multidimensional parameter space that involves, in addition to $M_X$ and $\alpha_X$, the Hubble rate at the end of inflation, the reheating efficiency, and the non-minimal coupling of the Higgs with curvature