Towards a complete scheme of cosmological neutrino self-interactions: Collision term for a wide range of mediator masses

Neutrino self-interactions (NSI) offer a potential pathway to address anomalies in standard cosmology and explain existing cosmological tensions. In this work, we present a novel framework to obtain the neutrino--neutrino collision term within the Boltzmann hierarchy, incorporating both neutrino and mediator masses as free parameters. Our calculations encompass both Dirac-like and Majorana neutrinos and distinguish between two neutrino mass eigenstates. This work provides a valuable tool for future analyses, should a NSI signal be detected. Remarkably, our results show a smooth transition from the light to the heavy mediator approximation as the Universe cools down for non-resonant cases. Thus, for the widely studied heavy mediator, our new scheme eliminates the need to approximate at high redshifts when the temperature increases above the mediator mass, and it provides the tools to test the threshold of validity of the heavy mediator paradigm. While this work focuses on NSI mediated by a scalar particle, the presented framework could be adapted to a broader range of neutrino NSI and possibly to warm dark matter self-interacting scenarios.