Cosmological Behavior of a Parity and Charge-Parity Violating Varying Alpha Theory

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.