Probing the Cosmic Neutrino Background and New Physics with TeV-Scale Astrophysical Neutrinos

We use recent evidence of TeV neutrino events from the most significant astrophysical sources detected by IceCube -- NGC 1068, TXS 0506+056, PKS 1424+240 -- to constrain the local and global overdensity of relic neutrinos and to explore potential new neutrino self-interactions. Assuming a relic neutrino overdensity, such high-energy neutrinos have travelled considerable distances through a sea of relic neutrinos and could have undergone scattering, altering their observed flux on Earth. Considering only Standard Model interactions, we constrain the relic overdensity to $\eta \leq 2 \times 10^{14}$ at the 90$\%$ confidence level, assuming the sum of neutrino masses saturates the cosmological bound, $\sum_i m_i = 0.13$ eV. We demonstrate that this limit improves for larger neutrino masses and study how it depends on the scale of the overdensity region. Considering new interactions between TeV-scale neutrinos and relic neutrinos, mediated by a light boson, we probe couplings of approximately $g \sim 10^{-2}$ with current data for a boson mass around the MeV scale. We demonstrate that this limit improves with larger neutrino masses and the scale of the overdensity region.