# Effect of collisions on neutrino flavor inhomogeneity in a dense neutrino gas

## TL;DR

This study explores how collisions influence the development of flavor inhomogeneities in a dense neutrino gas, revealing that collisions can suppress instabilities at small scales but not at large scales, especially for inverted mass hierarchy.

## Contribution

It provides new insights into the role of incoherent collisions in neutrino flavor stability, particularly highlighting scale-dependent effects and hierarchy differences.

## Key findings

- Collisions suppress flavor instability growth at small scales.
- Inverted hierarchy instabilities are resistant to suppression by collisions at large scales.
- Normal hierarchy shows broader instability range without collisions.

## Abstract

We investigate the stability, with respect to spatial inhomogeneity, of a two-dimensional dense neutrino gas. The system exhibits growth of seed inhomogeneity due to nonlinear coherent neutrino self-interactions. In the absence of incoherent collisional effects, we observe a dependence of this instability growth rate on the neutrino mass spectrum: the normal neutrino mass hierarchy exhibits spatial instability over a larger range of neutrino number density compared to that of the inverted case. We further consider the effect of elastic incoherent collisions of the neutrinos with a static background of heavy, nucleon-like scatterers. At small scales, the growth of flavor instability can be suppressed by collisions. At large length scales we find, perhaps surprisingly, that for inverted neutrino mass hierarchy incoherent collisions fail to suppress flavor instabilities, independent of the coupling strength.