Density and spin response function of a normal Fermi gas at unitarity

Using Landau theory of Fermi liquids we calculate the dynamic response of both a polarized and unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the {\it in phase} (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Viceversa, the {\it out of phase} (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.