  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
$\Lambda-$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.
