  We study collective excitations in a superfluid neutron gas at zero
temperature within the quasiparticle random phase approximation. The
particle-hole residual interaction is obtained from a Skyrme functional, while
a separable interaction is used in the pairing channel which gives a realistic
density dependence of the pairing gap. In accordance with the Goldstone
theorem, we find an ungapped collective mode (analogous to the
Bogoliubov-Anderson mode). At low momentum, its dispersion relation is
approximately linear and its slope coincides with the hydrodynamic speed of
sound calculated with the Skyrme equation of state. The response functions are
compared with those obtained within the Landau approximation. We also compute
the contribution of the collective mode to the specific heat of the neutron
gas, which is relevant for the thermodynamic properties of the inner crust of
neutron stars.
