Chaos, determinacy and fractals in active–sterile neutrino oscillations in the earlyuniverse

Abstract

The possibility of light sterile neutrinos allows for the resonant production of leptonnumber in the early universe through matter-affected neutrino mixing. For a given mixingof the active and sterile neutrino states it has been found that the lepton numbergeneration process is chaotic and strongly oscillatory. We undertake a new studyof the sensitivity of this process to initial conditions through the quantum rateequations. We confirm the chaoticity of the process in this solution, and moreoverfind that the resultant lepton number and the sign of the asymmetry produce afractal in the parameter space of mass, mixing angle and initial baryon number.This has implications for future searches for sterile neutrinos, where arbitrarilyhigh sensitivity may not be determinate in forecasting the lepton number of theuniverse.