We study the consequences on the neutrino oscillation parameter space, mixing angle ($\tan^2θ$) and vacuum mass difference ($Δm^2_0$), when mass varying neutrino (MaVaN) models are assumed in a supernova environment. We consider electronic to sterile channels $ν_e \rightarrow ν_s$ and $\barν_e \rightarrow \barν_s$ in two-flavor scenario. In a given model of MaVaN mechanism, we induce a position-dependent effective mass difference, $Δ\tilde m^2(r)$, where $r$ is the distance from the supernova core, that changes the neutrino and anti-neutrino flavour conversion probabilities. We study the constraints on the mixing angle and vacuum mass difference coming from r-process and the SN1987A data. Our result is the appearance of a new exclusion region for very small mixing angles, $\tan^2θ=10^{-6}-10^{-2}$, and small vacuum mass difference, $Δm^2_0=~1-20$ eV$^2$, due the MaVaN mechanism.

8 pages, 5 figures