Astrophysical simulations of supernovae and neutron stars demand as input microscopic calculations of thermodynamic and transport properties of nuclear matter with controlled uncertainty estimates. Effective Field Theory (EFT) provides a pertinent framework to address this problem. In the first part of this talk, we discuss new results for the ground-state energy of a dilute Fermi gas up to fourth order in pion-less EFT. Special attention is paid to the decrease of the convergence of the EFT with increasing density.
In the second part, we then discuss the chiral EFT approach to the nuclear many-body problem. In particular, we investigate the impact of different three-body contributions on thermodynamic properties of nuclear matter.