PTOLEMY's test of generalized neutrino interactions: unveiling challenges and constraints

Unanswered questions surrounding neutrinos have motivated investigations into physics beyond the standard model (SM) of particle physics. In particular, generalized neutrino interactions (GNI) provide a broader framework for studying these effects compared to the commonly studied non-standard neutrino interactions. These interactions are described by higher dimensional operators while maintaining the gauge symmetries of the SM. Furthermore, the cosmic neutrino background, a predicted component of the SM and standard cosmology, has yet to be directly detected. To shed light on this elusive phenomenon, we conduct a comprehensive analysis of the relevant GNI, specifically focusing on their implications for the proposed cosmic neutrino detector PTOLEMY. We make an attempt to see the capabilities and the limitations of PTOLEMY in sensing GNI while remaining optimistic regarding PTOLEMY's experimental resolution. These interactions play a significant role in modifying the electron spectrum resulting from the capture of cosmic neutrinos on radioactive tritium. This work also explores how the presence of these interactions influences the differential electron spectrum, taking into account factors such as finite experimental resolution, the mass of the lightest neutrino eigenstate, the strength of the interactions, and the ordering of neutrino mass.