  The neutron-matter equation of state constrains the properties of many
physical systems over a wide density range and can be studied systematically
using chiral effective field theory (EFT). In chiral EFT, all many-body forces
among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO).
We present details and additional results of the first complete N3LO
calculation of the neutron-matter energy, which includes the subleading
three-nucleon as well as the leading four-nucleon forces, and provides
theoretical uncertainties. In addition, we discuss the impact of our results
for astrophysics: for the supernova equation of state, the symmetry energy and
its density derivative, and for the structure of neutron stars. Finally, we
give a first estimate for the size of the N3LO many-body contributions to the
energy of symmetric nuclear matter, which shows that their inclusion will be
important in nuclear structure calculations.
