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 ∼10−32 c. Stronger constraints (or observable effects!) can arise from optical measurements of distant sources.