Cosmological CPT Violation and CMB Polarization Measurements
  In this paper we study the possibility of testing Charge-Parity-Time Reversal
(CPT) symmetry with cosmic microwave background (CMB) experiments. We consider
two kinds of Chern-Simons (CS) term, electromagnetic CS term and gravitational
CS term, and study their effects on the CMB polarization power spectra in
detail. By combining current CMB polarization measurements, the seven-year
WMAP, BOOMERanG 2003 and BICEP observations, we obtain a tight constraint on
the rotation angle $\Delta\alpha=-2.28\pm1.02$ deg ($1\,\sigma$), indicating a
$2.2\,\sigma$ detection of the CPT violation. Here, we particularly take the
systematic errors of CMB measurements into account. After adding the QUaD
polarization data, the constraint becomes $-1.34<\Delta\alpha<0.82$ deg at 95%
confidence level. When comparing with the effect of electromagnetic CS term,
the gravitational CS term could only generate TB and EB power spectra with much
smaller amplitude. Therefore, the induced parameter $\epsilon$ can not be
constrained from the current polarization data. Furthermore, we study the
capabilities of future CMB measurements, Planck and CMBPol, on the constraints
of $\Delta\alpha$ and $\epsilon$. We find that the constraint of $\Delta\alpha$
can be significantly improved by a factor of 15. Therefore, if this rotation
angle effect can not be taken into account properly, the constraints of
cosmological parameters will be biased obviously. For the gravitational CS
term, the future Planck data still can not constrain $\epsilon$ very well, if
the primordial tensor perturbations are small, $r <0.1$. We need the more
accurate CMBPol experiment to give better constraint on $\epsilon$.
