Can active-sterile neutrino oscillations lead to chaotic behavior of the cosmological lepton asymmetry?

TL;DR

This paper investigates whether active-sterile neutrino oscillations can cause chaotic behavior in the cosmological lepton asymmetry, using full momentum-dependent quantum kinetic equations, and finds that the sign of the asymmetry is deterministic with higher resolution.

Contribution

It demonstrates that the sign of the lepton asymmetry is deterministic when solving the full quantum kinetic equations with high resolution, challenging previous conjectures of chaos.

Findings

Oscillations in lepton asymmetry are eliminated at higher resolution.

The sign of the lepton asymmetry is deterministic, not chaotic.

Introduces the adaptive solver LASAGNA for quantum kinetic equations.

Abstract

While the cosmic baryon asymmetry has been measured at high accuracy to be 6.1*10^-10, a corresponding lepton asymmetry could be as large as 10^-2 if it hides in the neutrino sector. It has been known for some time that a large asymmetry can be generated from a small initial asymmetry given the existence of a sterile neutrino with a mass less than the mass of the active neutrino. While the magnitude of the final lepton asymmetry is deterministic, its sign has been conjectured to be chaotic in nature. This has been proven in the single momentum approximation, also known as the quantum rate equations, but has up to now not been established using the full momentum dependent quantum kinetic equations. Here we investigate this problem by solving the quantum kinetic equations for a system of 1 active and 1 sterile neutrino on an adaptive grid. We show that by increasing the resolution oscillations in the lepton asymmetry are eliminated and that the sign of the lepton asymmetry is in fact deterministic. This paper also serves as a launch paper for the adaptive solver LASAGNA which is available at http://users-phys.au.dk/steen.