Birefringence, CMB polarization and magnetized B-mode

Even in the absence of a sizable tensor contribution, a B-mode polarization can be generated because of the competition between a pseudo-scalar background and pre-decoupling magnetic fields. By investigating the dispersion relations of a magnetoactive plasma supplemented by a pseudo-scalar interaction, the total B-mode polarization is shown to depend not only upon the plasma and Larmor frequencies but also on the pseudo-scalar rotation rate. If the (angular) frequency channels of a given experiment are larger than the pseudo-scalar rotation rate, the only possible source of (frequency dependent) B-mode autocorrelations must be attributed to Faraday rotation. In the opposite case the pseudo-scalar contribution dominates and the total rate becomes, in practice, frequency-independent. The B-mode cross-correlations can be used, under certain conditions, to break the degeneracy by disentangling the two birefringent contributions. In the ΛCDM paradigm a potential candidate for the B-mode polarization are the tensor modes of the geometry inducing a frequency-independent polarization of the Cosmic Microwave Background (CMB in what follows). By frequency-independent signal we mean that different observational channels measure angular power spectra with the same amplitude. In the opposite case the angular power spectra will effectively depend upon the (angular) frequency of observation. The WMAP 5-yr data [1] constrain the presence of a B-mode and, indirectly, rT, i.e. the ratio of the tensor power spectrum over the scalar power spectrum [1]. A further (frequency independent) source of B-mode polarization is cosmic shear (see e.g. [2]). Diverse data sets (such as the ones of Quad and Capmap [3]) impose concurrent limits on the B-mode polarization. Forthcoming experiments are expected to improve the present status of the observations by reaching into the region rT < 0.2. The only frequency-dependent signal investigated so far is provided by the Faraday effect which is a distinctive feature of magnetized plasmas in different contexts [4]. Large-scale magnetic fields present prior to the equality time are known to impact both on the temperature autocorrelations as well as on the polarization observables [5]. It has been recently shown, within a dedicated numerical approach [6], that the Faraday rotation signal induced by a pre-decoupling magnetic field can overwhelm the B-mode polarization induced by the standard tensor contribution [7]. The B-mode autocorrelations might not be always sufficient to infer the presence of a pre-equality magnetic field. In short, the idea is the following. Consider a set-up where the pre-equality plasma is birefringent because of the concurrent presence of a pseudo-scalar background field, be it σ, and of a large-scale magnetic field. Absent any pseudo-scalar background, the rotation rate would scale with the square of the wavelength [4] of the observational channel. In the presence of a pseudo-scalar field the dispersion relations can be generalized and the total rotation rate will have, both, a magnetic and a pseudo-scalar contribution. The purpose of this paper is to compute the B-mode polarization generated by the competition of the two aforementioned effects and to scrutinize if (and when) the two effects can be, at least partially, disentangled. The essentials of the problem at hand are usefully introduced in terms of the electromagnetic part of the action Sem = − 1 16π ∫