Improved limits on photon velocity oscillations

The mixing of the photon with a hypothetical sterile paraphotonic state would have consequences on the cosmological propagation of photons. The absence of distortions in the optical spectrum of distant Type Ia supernov\ae allows to extend by two orders of magnitude the previous limit on the Lorentz-violating parameter $\delta$ associated to the photon-paraphoton transition, extracted from the abscence of distortions in the spectrum of the cosmic microwave background. The new limit is consistent with the interpretation of the dimming of distant Type Ia supernov\ae as a consequence of a nonzero cosmological constant. Observations of gamma-rays from active galactic nuclei allow to further extend the limit on $\delta$ by ten orders of magnitude.