Cosmogenic neutrinos through the GRAND lens unveil the nature of cosmic accelerators

The sources of cosmic rays with energies above 55 EeV are still mysterious. A guaranteed associated flux of ultra high energy neutrinos known as the cosmogenic neutrino flux will be measured by next generation radio facilities, such as the proposed Giant Radio Array for Neutrino Detection (GRAND). By using the orthogonal information provided by the cosmogenic neutrino flux, we here determine the prospects of GRAND to constrain the source redshift evolution and the chemical composition of the cosmic ray sources. If the redshift evolution is known, independently on GRAND's energy resolution, GRAND with 200,000 antennas will constrain the proton/iron fraction to the similar to 5-10% level after one year of data taking; on the other hand, if hints on the average source composition are given, GRAND will measure the redshift evolution of the sources to a similar to 10% uncertainty. However, the foreseen configuration of GRAND alone will not be able to break the degeneracy between redshift evolution of the sources and their composition. Our findings underline the discriminating potential of next generation radio array detectors and motivate further efforts in this direction.