For a significant fraction of the history of the universe, neutrinos freely fall through spacetime. While they only weakly interact with matter, neutrinos have a significant impact in astrophysics. Experimental neutrino physics and observational cosmology are amidst an interesting era, where precision measurements in both fields have significantly improved scientific understanding of the standard model of particle physics and of the universe. Experiments in neutrino physics have not only discerned that neutrinos are massive particles, but have also measured their relative masses (but not their absolute masses) and the quantum mechanical mixing matrix that is a consequence of these differing mass scales. Meanwhile, precision cosmological observations have determined the energy content of the universe, which in turn has presented a self-consistent story of the history and evolution of the universe and its contents. The topics discussed in this dissertation are based upon an interplay between these two fields, at times pushing the envelope, but always focused upon the basic physical processes that affect massive neutrinos in an expanding universe. A hearty, pedagogical introduction is presented to highlight the relevant neutrino physics described in this work and an overview of cosmology, strongly biased toward the early universe, the paradigm in which much of the work in this dissertation is based. Sterile neutrinos in different regimes of mass and mixing with active neutrinos are proposed as well as asymmetries between the number density of active neutrinos and antineutrinos in the early universe. The consequences of these two propositions are discussed in terms of observables such as primordial light element abundances and the observables related to a sterile neutrino dark matter candidate. Neutrino emission from high-entropy electron-positron plasmas are introduced, and the effects of this large flux of neutrinos and antineutrinos on hot hydrogen burning are explored. Finally, the nature of the cosmic neutrino background, a relic of the hot Big Bang, is discussed as they freely fall through spacetime from weak decoupling to the present epoch.