Applications of chiral three-nucleon forces up to N³LO to nuclear matter

We have developed recently an improved method for including normal-ordered three-nucleon (3N) forces to many-body calculations of nuclear matter. Applying these density-dependent effective two-body forces to matter of arbitrary proton fractions we show results for the equation of state based on chiral N³LO two- and N²LO three-body forces up second order and study the symmetry energy including contributions beyond the quadratic expansion. As our method allows to incorporate also the recent developed matrix elements of the subleading three-body forces we show in addition results for consistent N³LO calculations of pure neutron matter at zero temperature. Furthermore, these advances in treating chiral 3N forces up to N³LO can directly be used for advanced studies of properties of neutron matter, such as the equation of state based on the nonperturbative approach of self-consistent Green's functions or the ³PF₂ BCS energy gap. We show first results for these.