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.

Standard models describing the radiation transfer of the cosmic microwave background (CMB) through Compton scattering predict that cosmological scalar perturbations at linear order are not able to source V and B polarization modes. In this work we investigate the possibility that such CMB polarization modes are generated even in the presence of linear scalar perturbations only. We provide a general parametrization of the photon-fermion forward-scattering amplitude and compute mixing terms between different CMB polarization modes. We discuss different general extensions of Standard Model interactions which violate discrete symmetries, while preserving the combination of charge conjugation, parity and time reversal. We show that it is possible to source CMB circular polarization by violating parity and charge conjugation symmetries. Instead, B-mode generation is associated to the violation of symmetry for time-reversal. Our results provide a useful tool to constrain new physics using CMB data.

Recent literature has shown that photon-photon forward scattering mediated by Euler-Heisenberg interactions may generate some amount of the circular polarization (V modes) in the cosmic microwave background (CMB) photons. However, there is an apparent contradiction among the different references about the predicted level of the amplitude of this circular polarization. In this work, we will resolve this discrepancy by showing that with a quantum Boltzmann equation formalism, we obtain the same amount of circular polarization as using a geometrical approach that is based on the index of refraction of the cosmological medium. We will show that the expected amplitude of V modes is expected to be ≈8 orders of magnitude smaller than the amplitude of E-polarization modes that we actually observe in the CMB, thus confirming that it is going to be challenging to observe such a signature. Throughout the paper, we also develop a general method to study the generation of V modes from photon-photon and photon-spin-1massive-particle forward scatterings without relying on a specific interaction, which thus represent possible new signatures of physics beyond the Standard Model.

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