  We explore the use of mean field models to approximate microscopic nuclear
equations of state derived from chiral effective field theory across the
densities and temperatures relevant for simu- lating astrophysical phenomena
such as core-collapse supernovae and binary neutron star mergers. We consider
both relativistic mean field theory with scalar and vector meson exchange as
well as energy density functionals based on Skyrme phenomenology and compare to
thermodynamic equa- tions of state derived from chiral two- and three-nucleon
forces in many-body perturbation theory. Quantum Monte Carlo simulations of
symmetric nuclear matter and pure neutron matter are used to determine the
density regimes in which perturbation theory with chiral nuclear forces is
valid. Within the theoretical uncertainties associated with the many-body
methods, we find that select mean field models describe well microscopic
nuclear thermodynamics. As an additional consistency requirement, we study as
well the single-particle properties of nucleons in a hot/dense environment,
which affect e.g., charged-current weak reactions in neutron-rich matter. The
identified mean field models can be used across a larger range of densities and
temperatures in astrophysical simulations than more computationally expensive
microscopic models.
