  We study the spin response of cold dense neutron matter in the limit of zero
momentum transfer, and show that the frequency dependence of the
long-wavelength spin response is well constrained by sum-rules and the
asymptotic behavior of the two-particle response at high frequency. The
sum-rules are calculated using Auxiliary Field Diffusion Monte Carlo technique
and the high frequency two-particle response is calculated for several
nucleon-nucleon potentials. At nuclear saturation density, the sum-rules
suggest that the strength of the spin response peaks at $\omega \simeq$ 40--60
MeV, decays rapidly for $\omega \geq $100 MeV, and has a sizable strength below
40 MeV. This strength at relatively low energy may lead to enhanced neutrino
production rates in dense neutron-rich matter at temperatures of relevance to
core-collapse supernova.
