  We compute singlet pairing gaps and critical temperatures in pure neutron
matter with different many-body approximations. Medium effects tend to reduce
gaps and critical temperatures compared to the standard BCS ansatz. In the
mean-field approximation, the ratio of these two quantities remains constant
across a wide range of densities. This constant ratio is close to the universal
prediction of BCS theory, whether three-neutron interactions are included or
not. Using a more sophisticated many-body approach that incorporates the effect
of short-range correlations in pairing properties, we find that the gap to
critical temperature ratio in the low-density regime is substantially larger
than the BCS prediction, independently of the interaction. In this region, our
results are relatively close to experiments and theoretical calculations from
the unitary Fermi gas. We also find evidence for a different density dependence
of zero-temperature gaps and critical temperatures in neutron matter.
