Extended axion electrodynamics: Optical activity induced by   nonstationary dark matter
  We establish a new self-consistent Einstein-Maxwell-axion model based on the Lagrangian, which is linear in the pseudoscalar (axion) field and its four-gradient and includes the four-vector of macroscopic velocity of the axion system as a whole. We consider extended equations of the axion electrodynamics, modified gravity field equations, and discuss nonstationary effects in the phenomenon of optical activity induced by axions. 
A.B. Balakin and N.O. Tarasova
gr-qc astro-ph.CO hep-th