New Constraints on Cosmic Polarization Rotation from B-Mode Polarization
  in Cosmic Microwave Background
  STPpol, POLARBEAR and BICEP2 have recently measured the cosmic microwave
background (CMB) B-mode polarization in various sky regions of several tens of
square degrees and obtained BB power spectra in the multipole range 20-3000,
detecting the components due to gravitational lensing and to inflationary
gravitational waves. We analyze jointly the results of these three experiments
and propose modifications of their analysis of the spectra to include in the
model, in addition to the gravitational lensing and the inflationary
gravitational waves components, also the effects induced by the cosmic
polarization rotation (CPR), if it exists within current upper limits. Although
in principle our analysis would lead also to new constraints on CPR, in
practice these can only be given on its fluctuations <{\delta}{\alpha}^2>,
since constraints on its mean angle are inhibited by the de-rotation which is
applied by current CMB polarization experiments, in order to cope with the
insufficient calibration of the polarization angle. The combined data fits from
all three experiments (with 29% CPR-SPTpol correlation, depending on
theoretical model) gives constraint <{\delta}{\alpha}^2>^1/2 < 27.3 mrad
(1.56{\deg}) with r = 0.194 \pm 0.033. These results show that the present data
are consistent with no CPR detection and the constraint on CPR fluctuation is
about 1.5{\deg}. This method of constraining the cosmic polarization rotation
is new, is complementary to previous tests, which use the radio and optical/UV
polarization of radio galaxies and the CMB E-mode polarization, and adds a new
constraint for the sky areas observed by SPTpol, POLARBEAR and BICEP2.
