  Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong
interactions, spin-orbit coupling and multi-band anisotropy predict chiral or
helical ground states with strong anisotropy of the pairing states, with deep
minima in the excitation gap, as well as strong phase anisotropy for the chiral
ground state. We develop time-dependent mean field theory to calculate the
Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A
to chiral superconductors with strong anisotropy. Chiral superconductors
support a pair of massive Bosonic excitations of the time-reversed pairs
labeled by their parity under charge conjugation. These modes are degenerate
for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong
anisotropy also leads to low-lying Fermions, and thus to channels for the decay
of the Bosonic modes. Selection rules and phase space considerations lead to
large asymmetries in the lifetimes and hybridization of the Bosonic modes with
the continuum of un-bound Fermion pairs. We also highlight results for the
excitation of the Bosonic modes by microwave radiation that provide clear
signatures of the Bosonic modes of an anisotropic chiral ground state.
