Photon-Axion-Like Particle Coupling Constant and Cosmological   Observations
  We estimated the photon-pseudoscalar particle mixing constant from the effect of cosmological alignment and cosmological rotation of polarization plane of distant QSOs. This effect is explained in terms of birefringent phenomenon due to photon-pseudoscalar (axion-like) particle mixing in a cosmic magnetic field. On the contrary, one can estimate the strength of the cosmic magnetic field using the constraints on the photon-axion-like particle coupling constant from the CAST experiment and from SNe Ia dimming effect. In a result, the lower limit on the intergalactic ($z\approx 1\div 2$) magnetic field appears at the level of about $4\times 10^{-10}\div 10^{-11}$ G. 
M. Yu. Piotrovich, Yu. N. Gnedin, T. M. Natsvlishvili