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We discuss the rotation of the linear polarization plane and the productionof circular polarization generated by a pseudoscalar field acting as darkmatter. We compute analytically and numerically the propagation of the Stokesparameters from the last scattering surface for an oscillating and a monotonicdecreasing pseudoscalar field. For the models studied in this paper, we showthe comparison between the widely used approximation in which the rotationangle is constant in time and the exact result.

Rotation of Linear Polarization Plane and Circular Polarization from Cosmological Pseudoscalar Fields