Cosmic horizon of neutrinos

The persistent discrepancy between the experimental measurement and the Standard Model (SM) prediction of the muon’s anomalous magnetic moment ( g − 2 ) μ remains one of the most intriguing hints of physics beyond the SM. A well-motivated explanation involves a light Z ′ gauge boson associated with a broken U ( 1 ) L μ − L τ symmetry. Such a boson not only resolves the ( g − 2 ) μ anomaly, but also induces resonant interactions between high-energy cosmic neutrinos and the cosmic neutrino background ( C ν B ), potentially shaping the observable neutrino flux at Earth. In this work, we explore the implications of such interactions for the cosmic propagation of high-energy neutrinos. We compute the optical depth for neutrino attenuation via Z ′ -mediated scattering, accounting for neutrino masses, hierarchies, and thermal distributions. We delineate the regions in ( m Z ′ , m ν ) space where the optical depth exceeds unity, defining a “neutrino cosmic horizon” beyond which high-energy neutrinos are significantly attenuated. We confront these results with the parameter space required to simultaneously explain the muon g − 2 anomaly and ease the Hubble tension via an additional contribution to the effective number of relativistic degrees of freedom, Δ N eff ≃ 0.2 – 0.5 . Our analysis reveals a consistent region in parameter space where all three phenomena ( g − 2 ) μ , N eff , and high-energy neutrino attenuation can be explained by the same light mediator. These findings motivate future searches for spectral features in IceCube and its next-generation successors as indirect probes of new physics in the neutrino sector.