Chaos, Determinacy and Fractals in Active-Sterile Neutrino Oscillations in the Early Universe

TL;DR

This paper investigates the chaotic and fractal behavior of lepton number generation via active-sterile neutrino oscillations in the early universe, revealing sensitivity to initial conditions and implications for sterile neutrino searches.

Contribution

It demonstrates the chaotic nature of lepton number production and uncovers fractal structures in parameter space, advancing understanding of neutrino oscillation dynamics in cosmology.

Findings

Lepton number generation is chaotic and oscillatory.

Fractal structures are found in parameter space.

High sensitivity limits predictability of lepton asymmetry.

Abstract

The possibility of light sterile neutrinos allows for the resonant production of lepton number in the early universe through matter-affected neutrino mixing. For a given a mixing of the active and sterile neutrino states it has been found that the lepton number generation process is chaotic and strongly oscillatory. We undertake a new study of this process' sensitivity to initial conditions through the quantum rate equations. We confirm the chaoticity of the process in this solution, and moreover find that the resultant lepton number and the sign of the asymmetry produces a fractal in the parameter space of mass, mixing angle and initial baryon number. This has implications for future searches for sterile neutrinos, where arbitrary high sensitivity could not be determinate in forecasting the lepton number of the universe.