  Cosmogenic neutrinos originate from interactions of cosmic rays propagating
through the universe with cosmic background photons. Since both high-energy
cosmic rays and cosmic background photons exist, the existence of high-energy
cosmogenic neutrinos is almost certain. However, their flux has not been
measured so far. Therefore, we calculated the flux of high-energy cosmogenic
neutrinos arriving at the Earth on the basis of elaborate four-dimensional
simulations that take into account three spatial degrees of freedom and the
cosmological time-evolution of the universe. Our predictions for this neutrino
flux are consistent with the recent upper limits obtained from large-scale
cosmic-ray experiments. We also show that the extragalactic magnetic field has
a strong influence on the neutrino flux. The results of this work are important
for the design of future neutrino observatories, since they allow to assess the
detector volume that is necessary to detect high-energy cosmogenic neutrinos in
the near future. An observation of such neutrinos would push multimessenger
astronomy to hitherto unachieved energy scales.
