  A previous study of nuclear matter in a chiral nucleon-meson model is
extended to isospin-asymmetric matter. Fluctuations beyond mean-field
approximation are treated in the framework of the functional renormalization
group. The nuclear liquid-gas phase transition is investigated in detail as a
function of the proton fraction in asymmetric matter. The equations of state at
zero temperature of both symmetric nuclear matter and pure neutron matter are
found to be in good agreement with realistic many-body computations. We also
study the density dependence of the pion mass in the medium. The question of
chiral symmetry restoration in neutron matter is addressed; we find a
stabilization of the phase with spontaneously broken chiral symmetry once
fluctuations are included. Finally, neutron star matter including beta
equilibrium is discussed. The model satisfies the constraints imposed by the
existence of two-solar-mass neutron stars.
