Including birefringence into time evolution of CMB: current and future
  constraints
  We introduce birefringence effects within the propagation history of CMB,
considering the two cases of a constant effect and of an effect that increases
linearly in time, as the rotation of polarization induced by birefringence
accumulates during photon propagation. Both cases result into a mixing of E and
B modes before lensing effects take place, thus leading to the fact that
lensing is acting on spectra that are already mixed because of birefringence.
Moreover, if the polarization rotation angle increases during propagation,
birefringence affects more the large scales that the small scales. We put
constraints on the two cases using data from WMAP 9yr and BICEP 2013 and
compare these results with the constraints obtained when the usual procedure of
rotating the final power spectra is adopted, finding that this dataset
combination is unable to distinguish between effects, but it nevertheless hints
for a non vanishing value of the polarization rotation angle. We also forecast
the sensitivity that will be obtained using data from Planck and PolarBear,
highlighting how this combination is capable to rule out a vanishing
birefringence angle, but still unable to distinguish the different scenarios.
Nevertheless, we find that the combination of Planck and PolarBear is sensitive
enough to highlight the existence of degeneracies between birefringence
rotation and gravitational lensing of CMB photons, possibly leading to false
detection of non standard lensing effects if birefringence is neglected.
