Statistical Isotropy violation of CMB polarization sky due to Lorentz
  boost
  In the frame of a moving observer, the Cosmic Microwave Background (CMB)
fluctuation exhibits violation of Statistical Isotropy (SI). The SI violation
effect from our local motion on CMB temperature fluctuation has been measured
in the recent Planck results. We calculate the effect of our local motion with
velocity $(\beta \equiv |\boldsymbol v|/c= 1.23 \times 10^{-3})$ on CMB
polarization field. The Lorentz transformation of the polarization field leads
to aberration in the direction of incoming photons and also modulation of the
Stokes parameters, which results in mixing of power between different CMB
multipoles. We show that for small values of $\beta$, the effect on the angular
power spectra that corresponds to the diagonal terms in the spherical harmonic
space is at $O(\beta^2)$. But non-zero off-diagonal terms at the linear order
in $\beta$ could provide a measurable signature of SI violation in the Bipolar
Spherical Harmonic (BipoSH) representation. We also calculate the measurability
of $\beta$ from polarization maps from experiments like Planck and PRISM. It is
possible to measure $\beta$ from the ideal, cosmic variance limited BipoSH
spectra of $EE$, $TE$, $BB$, but not in $EB$ and $TB$. With the instrumental
noise of and angular resolution of Planck, it is not possible to measure
$\beta$ with high statistical significance from BipoSH spectra of polarization.
PRISM can measure $\beta$ with high significance in both $EE$ and $TE$ BipoSH
spectra, but not in $BB$, $EB$ and $TB$ BipoSH spectra.
