QCD axion couplings at finite density

After reviewing the foundational aspects of quantum field theory at finite density, the thesis focusses on the modifications of axion properties in systems at finite baryonic density. Those are especially relevant for highly dense stellar environments such as Supernovae and neutron stars, which are typically employed to set stringent limits on axion couplings from anomalous stellar cooling. Specifically, we consider finite density modifications of axion couplings to nucleons within the framework of heavy baryon chiral perturbation theory and assess their consequences for astrophysical constraints on the axion parameter space.