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.