Recent advances in experiments and theory of cold atomic gases, and in
neutron star observations, yield important new insights on the equation of
state of neutron matter. At low densities, neutron matter is a strongly
paired Fermi system, with pairing gaps of up to 1/3 the Fermi energy.
The equation of state and the properties of inhomogeneous neutron matter
at low to moderate densities are very important to describing the neutron
star crust; and microscopic calculations can put severe constraints on
density functionals used to describe the crust.
At higher densities the EOS plays a critical role in determining the
mass-radius relationship for neutron stars, and is very sensitive to the
three- neutron interaction. Microscopic calculations with realistic
2- and 3-nucleon interactions make clear predictions for terrestrial
experiments, giving a definite relation between the energy of neutron
matter at saturation density and its density dependence, and predictions
for astrophysical observations, including the maximum mass and radius
for a neutron star given a specified symmetry energy.