We present an analytic derivation of the diffuse spectra for high energy neutrinos (E > PeV), produced by the propagation of ultra-high energy protons in astrophysical photon backgrounds (cosmogenic neutrinos). We address several scenarios of cosmological transport based on homogeneous distribution of sources with a generic cosmological evolution. By utilizing recent cross-section models, we compute the local neutrino emissivity and finally the expected neutrinos flux at redshift z=0.
Beyond its pedagogical value, this result yields essential insights into estimating the uncertainties associated with these predictions. Furthermore, it serves as a reliable benchmark for more advanced calculations conducted using modern numerical codes such as SimProp and CRPropa.