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Influence of cosmological models on the GZK horizon of ultrahigh energy protons

We investigate how the density of baryonic and cold dark matter, the density of dark energy and the value of the Hubble parameter at the present time influence the propagation of ultrahigh energy protons in the nearby Universe. We take into account energy losses in the cosmic microwave radiation, the only one relevant for protons above $10^{18}$ eV, and we explore the dependence of Greisen-Zatsepin-Kuz'min (GZK) horizon on the cosmology. We investigate several cosmological scenarios, from matter dominated to energy dominated ones, and we consider the impact of uncertainties in the Hubble parameter in a $Λ-$Cold Dark Matter (CDM) Universe, estimated from recent observations, on the GZK horizon. The impact of the (unknown) extragalactic magnetic field on our study is discussed, as well as possible probes of the Hubble parameter attainable by current and future experiments.