Do Finite Density Effects Jeopardize Axion Nucleophobia in Supernovae?

Nucleophobic axion models, wherein axion couplings to both protons and neutrons are simultaneously suppressed, can relax the stringent constraints from SN 1987A. However, it remains uncertain whether these models maintain their nucleophobic property under the influence of finite baryon density effects. These are especially relevant in astrophysical environments near saturation density, such as Supernovae (SNe). In this study, we demonstrate that the nucleophobic solution remains viable also at finite density. Furthermore, we show that the SN axion bound relaxes significantly in nucleophobic models, even when accounting for the integration over the non-homogeneous environment of the SN core.