  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.
