  In this report we construct a phenomenological model in which the time
variation of the fine structure constant, $\alpha$, is induced by a parity and
charge-parity (PCP) violating interaction. Such a PCP violation in the photon
sector has a distinct physical origin from that in the conventional models of
this kind. We calculate the cosmological birefringence so induced in our model
and show that it in turn produces a new non-vanishing multipole moment
correlation between the temperature and the polarization anisotropies in the
CMB spectrum. We have also calculated the amount of optical rotation due to a
strong background magnetic field and the effect of our new PCP violating term
on the variation of $\alpha$ during the cosmic evolution. We found that only in
the radiation dominated era can the contribution of the new PCP violating term
to the variation of $\alpha$ be non-vanishing.
