  We study the influence of population imbalance on the pairing, spin, and
density instabilities of a two component ideal Fermi gas after a sudden quench
of interactions near a Feshbach resonance. Over a large region of parameters
the pairing instability is dominated by finite momentum pairing, suggesting the
possibility of observing FFLO-like states in the unstable initial dynamics.
Long-wavelength density instabilities are found on the BCS side of the
resonance, and are interpreted as a precursor of the phase separation expected
at equilibrium. On the BEC side of the resonance, the pairing instability is
present for scattering lengths that are larger than a critical value that is
only weakly dependent on population imbalance and always smaller than the
scattering length at which the Stoner-like spin instability occurs.
