GRAPH mixing
  In the era of gravitational wave (GW) detection from astrophysical sources by
LIGO/VIRGO, it is of great importance to take the quantum gravity effect of
graviton-photon (GRAPH) mixing in the cosmic magnetic field to the next level.
In this work, we study such an effect and derive for the first time
perturbative solutions of the linearized equations of motions of the GRAPH
mixing in an expanding universe. In our formalism we take into account all
known standard dispersive and coherence breaking effects of photons such as the
Faraday effect, the Cotton-Mouton (CM) effect, and the plasma effects in the
cosmic magnetic field. Our formalism, applies to a cosmic magnetic field either
a uniform or a slowly varying non-homogeneous field of spacetime coordinates
with an arbitrary field direction. For binary systems of astrophysical sources
of GWs at extragalactic distances with chirp masses $M_\text{CH}$ of a few
solar masses, GW present-day frequencies $\nu_0\simeq 50-700$ Hz, and
present-day cosmic magnetic field amplitudes $\bar B_0\simeq 10^{-10}-10^{-6}$
G, the power of electromagnetic radiation generated in the GRAPH mixing at
present is substantial and in the range $P_\gamma\simeq 10^6-10^{15}$ (erg/s).
On the other hand, the associated power flux $F_\gamma$ is quite faint
depending on the source distance with respect to the Earth. Since in the GRAPH
mixing the velocities of photons and gravitons are preserved and are equal,
this effect is the only one known to us, whose certainty of the contemporary
arrival of GWs and electromagnetic radiation at the detector is guaranteed.
