  Gravitons are the quantum counterparts of gravitational waves in low-energy
theories of gravity. Using Feynman rules one can compute scattering amplitudes
describing the interaction between gravitons and other fields. Here, we
consider the interaction between gravitons and photons. Using the quantum
Boltzmann equation formalism, we derive fully general equations describing the
radiation transfer of photon polarization, due to the forward scattering with
gravitons. We show that the Q and U photon linear polarization modes couple
with the V photon circular polarization mode, if gravitons have anisotropies in
their power-spectrum statistics. As an example, we apply our results to the
case of primordial gravitons, considering models of inflation where an
anisotropic primordial graviton distribution is produced. Finally, we evaluate
the effect on cosmic microwave background (CMB) polarization, showing that in
general the expected effects on the observable CMB frequencies are very small.
However, our result is promising, since it could provide a novel tool for
detecting anisotropic backgrounds of gravitational waves, as well as for
getting further insight on the physics of gravitational waves.
