Lorentz-violation-induced vacuum birefringence and its astrophysical consequences

In the electromagnetism of loop quantum gravity, two helicities of a photon have different phase velocities and group velocities, termed as ``vacuum birefringence''. Two novel phenomenons, ``peak doubling'' and ``depolarization'', are expected to appear for a linearly polarized light from astrophysical sources. We show that the criteria to observe these two phenomenons are the same. Further, from recently observed γ-ray polarization from Cygnus X-1, we obtain an upper limit ~8.7×10^-12 for the Lorentz-violating parameter χ, which is the most firm constraint from well-known systems. We also suggest analyzing the possible existence of ``peak doubling'' through Fermi-LAT gamma-ray bursts.