"Low energy string theory predicts the existence of an axion field which can lead to cosmic birefringence. We solve the electromagnetic wave equations in the presence of such an axion and a dilaton field in order to determine their effect on the polarization of light. We find that the presence of dilaton field leads to a nontrivial modification of the final result. We comment on the possibility of discovering such an effect by observations of radio wave polarizations from distant radio galaxies and quasars. We have also determined the limits on the string theory parameters that are imposed by the current polarization data from distant quasars and radio galaxies."
In this paper, we have studied cosmic birefringence in the framework of perturbative four-dimensional heterotic string theory. Due to coupling between dilaton and axion in this theory, we have shown that the dilaton ﬁeld changes the birefringence produced by the axion ﬁeld in a nontrivial way. We obtained an approximate expression for the rotation in polarization predicted by heterotic string theory within the WKB approximation. We analysed the data for distant quasars and radio galaxies to determine if the eﬀect is present in the data. We ﬁnd a marginally signiﬁcant eﬀect. However the correlation is caused primarily by two largest redshift points and the eﬀect is lost after these points are eliminated. Hence we ﬁnd that the data does not show signiﬁcant correlation but the large redshift points are suggestive that a signal might exist. This should be thoroughly investigated by accummulating more data at the largest redshifts. We have also determined the limits on the string theory parameters that are imposed by the current polarization data from distant quasars and radio galaxies.
We, furthermore, like to point out that all these calculations were done taking dilaton as a massless scalar. As explained in the introduction, one of the biggest problem in string theory is to ﬁnd a mechanism to remove this massless dilaton from present day physics. One expects that a potential for dilaton will be generated in string theory through some non-perturbative eﬀects and the dilaton will sit at the minimum of the potential picking up a mass. As the mecanism of how precisely this should happen is still not clear in string theory, we have not dealt with such a scenario in this paper.