  We explore low-density neutron matter and its behavior in proximity to the
unitary limit. To that end, we construct unitary nucleon-nucleon potentials
with infinite 1S0 neutron-neutron scattering lengths. We discuss the Berstch
parameter in relation to results from ultra-cold atomic gases. Unitarity as a
constraint for neutron matter and the symmetry energy has been discussed in the
literature. We revisit some of those arguments and emphasize the relevance of
keeping a firm link with low-energy nuclear physics for robust predictions of
neutron-rich systems. Our predictions are obtained from realistic few-nucleon
forces based on chiral effective field theory at N3LO.
