Multi-Messenger Astrophysics with the Cosmic Neutrino Background

The massive neutrinos of the Cosmic Neutrino Background (C$\nu$B) are fundamental ingredients of the radiation-dominated early universe and are important non-relativistic probes of the large-scale structure formation in the late universe. The dominant source of anisotropies in the neutrino flux distribution on the sky are highly amplified integrals of metric perturbations encountered during the non-relativistic phase of the C$\nu$B. This paper numerically compares the line-of-sight methods for computing C$\nu$B anisotropies with the Einstein-Boltzmann hierarchy solutions in linear theory for a range of neutrino masses. Angular power spectra are computed that are relevant to a future polarized tritium target run of the PTOLEMY experiment. Correlations between the C$\nu$B sky maps and galactic survey data are derived using line-of-sight techniques and discussed in the context of multi-messenger astrophysics.