We reconsider the problem of the birefringence of electromagnetic (EM) waves in a medium consisting of a plasma and a $ ubar{ u}$-gas within the Standard Model of particle physics. The considered effect arises in such a medium due to the parity violation for the electroweak neutrino-electron interaction. Our recent calculations of the electroweak correction to the photon polarization operator in the electroweak plasma allow us to significantly improve some previous estimates of such effect in astrophysics. We estimate the rotary power for EM waves propagating in a non-relativistic plasma in the intergalactic space and interacting with the gas of relic neutrinos and antineutrinos there. We show that, in presence of a plasma, the EM wave birefringence effect in a $ ubar{ u}$-gas exceeds significantly that effect in a $ ubar{ u}$-gas in empty space considered earlier. These previous treatments of the birefringence relied on the calculations of the refraction index for on-shell photons in vacuum using the forward scattering amplitude $gamma uto gamma u$ with virtual charged leptons in Feynman diagrams. The possibility to observe experimentally the new effect suggested here is discussed.
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