Neutron matter from chiral two- and three-nucleon calculations up to N$^3$LO

Neutron matter is an ideal laboratory for nuclear interactions derived from chiral effective field theory since all contributions are predicted up to next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$) in the chiral expansion. By making use of recent advances in the partial-wave decomposition of three-nucleon ($3N$) forces, we include for the first time ${\mathrm{N}}^{3}\mathrm{LO} 3N$ interactions in many-body perturbation theory (MBPT) up to third order and in self-consistent Green's function theory (SCGF). Using these two complementary many-body frameworks we provide improved predictions for the equation of state of neutron matter at zero temperature and also analyze systematically the many-body convergence for different chiral EFT interactions. Furthermore, we present an extension of the normal-ordering framework to finite temperatures. These developments open the way to improved calculations of neutron-rich matter including estimates of theoretical uncertainties for astrophysical applications.