  We describe and implement a procedure for determining the couplings of a
Relativistic Mean-Field Theory (RMFT) that is optimized for application to
neutron star phenomenology. In the standard RMFT approach, the couplings are
constrained by comparing the theory's predictions for symmetric matter at
saturation density with measured nuclear properties. The theory is then applied
to neutron stars which consist of neutron-rich matter at densities ranging up
to several times saturation density, which allows for additional astrophysical
constraints. In our approach, rather than using the RMFT to extrapolate from
symmetric to neutron-rich matter and from finite-sized nuclei to uniform
matter, we fit the RMFT to properties of uniform pure neutron matter obtained
from chiral effective field theory. Chiral effective field theory incorporates
the experimental data for nuclei in the framework of a controlled expansion for
nuclear forces valid at nuclear densities and enables us to account for
theoretical uncertainties when fitting the RMFT. We construct four simple RMFTs
that span the uncertainties provided by chiral effective field theory for
neutron matter, and are consistent with current astrophysical constraints on
the equation of state. Our RMFTs can be used to model the properties of
neutron-rich matter across the vast range of densities and temperatures
encountered in neutron stars and their mergers.
