Neutrinos have shaped cosmic history in important ways. In early epochs, they left their mark on the expansion of the universe and the genesis of primordial nuclei. In more recent eras, their signature has been repeatedly etched into the explosive dynamics of massive stars and the chemical enrichment of the cosmos. In the guise of sterile neutrinos, they may even constitute the dark matter.
None of these roles is, as of yet, fully understood. Aside from the observational challenges, there are significant theoretical ones. Neutrinos are known to come in at least three different flavors, each of which interacts differently with other particles. They are also known to oscillate: due to quantum mechanics, a neutrino's flavor changes in the course of its propagation. The phenomenology that emerges in dense neutrino systems as a result of flavor oscillations is a frontier topic of precision cosmology and high-energy astrophysics. It is the focal point of this dissertation.
The central theme is nonlinearity. When a system is dense in neutrinos, kinetic behaviors can arise that differ dramatically from those in systems dense only in "ordinary" matter like electrons and nucleons. The key piece of microphysics in this regard is the forward scattering of neutrinos on one another, which causes the flavor evolution of any given neutrino to depend on the flavor states of all neutrinos that it crosses paths with. The chapters here explore some of the macroscopic consequences of this subtle quantum phenomenon, with applications to the lepton-asymmetric early universe, core-collapse supernovae, and sterile neutrino dark matter.