Neutrinos as a Probe of Ultra-High Energy Cosmic Rays

The search for astrophysical high-energy neutrinos is one of the pillars of multi-messenger astronomy. Neutrino production in extragalactic sources or the cosmic environment is intimately related to (and limited by) the observed emission of γ-rays and cosmic rays. We will review the various indirect neutrino limits that arise from this cosmic connection. So far, no high-energy neutrino source could be unambiguously identified. However, the strong limits on TeV to PeV neutrino emission set by this non-observation serve as an indirect constraint of candidate sources of cosmic rays. At the EeV energy scale the diffuse flux of cosmogenic neutrinos associated with the propagation of ultra-high energy cosmic rays in the cosmic radiation background seems to be the most promising candidate for a future detection. We will discuss its model dependence w.r.t. nuclear composition and evolution of the sources and provide simple bolometric scaling relations and lower limits.