Stability in MaVaN Models

Mass-varying neutrino (MaVaN) models propose a source of dark energy in a new scalar field called the acceleron. Recent work has shown that nonrelativistic neutrino fields in these theories are unstable to inhomogeneous fluctuations, and form structures that no longer behave as dark energy. One might expect that in multiple-neutrino models, the lighter species could continue to act as a source for the acceleron, generating dark energy without the help of heavier species. This paper shows that by considering the evolution of the acceleron field for a large class of models, the result of any neutrino component becoming unstable is that all components become unstable within a short time on cosmological scales. An alternate model employing a second scalar field in a hybrid potential is shown to have stable MaVaN dark energy even in the presence of unstable heavier components.