Cosmological Searches for Photon Velocity Oscillations
  We posit a second massless photon, uncoupled to known forms of matter but undergoing Lorentz non-invariant velocity mixing with ordinary photons. Our speculation within a speculation suffers from the sin of implausibility but enjoys the virtue of verifiability. To avoid unacceptable distortion of the well-measured microwave background spectrum, the velocity difference of the photons cannot exceed $\sim10^{-32} c$. Stronger constraints (or observable effects!) can arise from optical measurements of distant sources. 
Sheldon L. Glashow (Harvard)