Role of Matter Inhomogeneity on Fast Flavor Conversion of Supernova Neutrinos

We investigated the impact of a spatially varying matter potential $\lambda$, coming from neutrino-electron forward scattering, on the emergence of fast neutrino flavor conversion (FFC) triggered by the presence of zero crossings in the angular distribution of the neutrino electron lepton number (ELN). We find that FFC can be significantly affected as the spatial variation rate of $\lambda$ increases, and strong spatial variations can completely stabilize initially unstable systems. Using stability analysis based solely on initial conditions, we identified for the first time a critical variation rate above which no FFC occurs even if the flavor instability exists. By analyzing several representative matter profiles based on an 18 $M_{\odot}$ SN model, we show that spatially inhomogeneous $\lambda$ can suppress the occurrence of FFC associated with shallow ELN zero crossings in most of the SN's radial region, especially during the accretion phase. Our finding highlights the need to consider the impact of matter inhomogeneity in the development of improved SN models that aim to include the effect of neutrino flavor conversions.