We present a state-of-the-art prediction for cross sections of neutrino deep inelastic scattering (DIS) from nucleon at high neutrino energies, $E_\nu$, up to 1000 EeV ($10^{12}$ GeV).
Our calculations are based on the latest CT18 NNLO parton distribution functions (PDFs) and their associated uncertainties. In order to make predictions for the highest energies, we extrapolate the PDFs to small $x$ according to several procedures and assumptions, thus affecting the uncertainties at ultra-high $E_\nu$; we quantify the uncertainties corresponding to these choices. Similarly, we quantify the uncertainties introduced by the nuclear corrections which are required to evaluate neutrino-nuclear cross sections for the neutrino observatories.
These results can be applied to currently-running astrophysical neutrino observatories, such as IceCube and KM3NeT, as well as various future experiments which have been proposed.