Analysing the Effect on CMB in a Parity and Charge Parity Violating
  Varying Alpha Theory
  In this paper we study in detail the effect of our recently proposed model of
parity and charge-parity (PCP) violating varying alpha on the Cosmic Microwave
Background (CMB) photon passing through the intra galaxy-cluster medium (ICM).
The ICM is well known to be composed of magnetized plasma. According to our
model, the polarization and intensity of the CMB would be affected when
traversing through the ICM due to non-trivial scalar photon interactions. We
have calculated the evolution of such polarization and intensity collectively,
known as the stokes parameters of the CMB photon during its journey through the
ICM and tested our results against the Sunyaev-Zel'dovich (SZ) measurement on
Coma galaxy cluster. Our model contains a PCP violating parameter, $\beta$, and
a scale of alpha variation $\omega$. Using the derived constrained on the
photon-to-scalar conversion probability, ${\bar P}_{\gamma \rightarrow \phi}$,
for Coma cluster in ref.[34] we found a contour plot in the ($\omega,\beta$)
parameter plane. The $\beta =0$ line in this parameter space corresponds to
well-studied Maxwell-dilaton type models which has lower bound on $\omega
\gtrapprox 6.4 \times 10^{9}$ GeV. In general, as the absolute value of $\beta$
increases, lower bound on $\omega$ also increases. Our model in general
predicts the modification of the CMB polarization with a non-trivial dependence
on the parity violating coupling parameter $\beta$. However, it is
unconstrained in this particular study. We show that this effect can in
principle be detected in the future measurements on CMB polarization such that
$\beta$ can also be constrained.
