  We investigate the collective modes in the spin-orbit coupled Fermi gas with
repulsive s-wave interaction. The interplay between spin-orbit coupling and
atom-atom interactions plays the crucial role in the collective behaviors of
Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit coupled Fermi gas
has strongly correlated spin and density excitations. Within the scheme of
random phase approximation, we classify collective modes based on the symmetry
group and determine their properties via the poles of corresponding correlation
functions. Besides, the particle-hole continuum is obtained, where the
imaginary part of these correlation functions become non-vanishing. We make
comparisons with collective excitations in the ordinary Fermi liquid without
spin-orbit coupling and in a helical liquid, i.e., surface states of a three
dimensional topological insulator. We also propose an experimental protocol for
detecting these collective modes and discuss corresponding experimental
signatures in the ultracold Fermi gases experiment.
