  Polarizations of primordial gravitational waves can be relevant when
considering inflationary universe in modified gravity or when matter fields
survive during inflation. Such polarizations have been discussed in the
Bunch-Davies vacuum. Instead of taking into account dynamical generation of
polarizations of gravitational waves, in this paper, we consider polarized
initial states constructed from $SU(2)$ coherent states. We then evaluate the
power spectrums of the primordial gravitational waves in the states.
