We introduce several coordinate-invariant statistical procedures in order to test for alignment of polarizations of electromagnetic radiation from astrophysical sources. A large-scale alignment of optical polarizations from distant quasi-stellar objects (QSOs) has recently been observed by Hutsemékers and collaborators. The new statistical procedures are based on comparing polarizations at different angular coordinates by making a parallel transport. The results of these statistical procedures continue to support the existence of the large-scale alignment effect in the QSO optical polarization data. The alignment is found to be much more pronounced in the data sample with low degrees of polarization, p 2 per cent. This suggests that the alignment may be attributed to some propagation effect. The distance scale over which the alignment effect is dominant is found to be of order 1 Gpc. We also find that a very large-scale alignment is present in the large-redshift, z 1, data sample. In fact, the data sample with z 1 appears to be aligned over the entire celestial sphere. This alignment is seen independent of the degree of polarization of the sources. We discuss possible physical effects, such as extinction and pseudoscalar-photon mixing, which may be responsible for the observations.

We investigate the effect of axions on the polarization of electromagnetic waves as they propagate through astronomical distances. We analyze the change in the dispersion of the electromagnetic wave due to its mixing with axions. We find that this leads to a shift in polarization and turns out to be the dominant effect for a wide range of frequencies. We analyze whether this effect or the decay of photons into axions can explain the large scale anisotropies which have been observed in the polarizations of quasars and radio galaxies. We also comment on the possibility that the axion-photon mixing can explain the dimming of distant supernovae.

We present a detailed statistical study of the observed anisotropy in radio polarizations from distant extragalactic objects. This anisotropy was earlier found by Birch (1982) and reconfirmed by Jain & Ralston (1999) in a larger data set. A very strong signal was seen after imposing the cut |RM − RM| > 6 rad/m 2 , where RM is the rotation measure and RM its mean value. In this paper we show that there are several indications that this anisotropy cannot be attributed to bias in the data. We also find that a generalized statistic shows a very strong signal in the entire data without imposing the RM dependent cut. Finally we argue that an anisotropic background pseudoscalar field can explain the observations.

We propose a new method for the extraction of Rotation Measure from spectral polarization data. The method is based on maximum likelihood analysis and takes into account the circular nature of the polarization data. The method is unbiased and statistically more efficient than the standard χ 2 procedure. We also find that the method is computationally much faster than the standard χ 2 procedure if the number of data points are very large.