Photon-graviton scattering: A new way to detect anisotropic gravitational waves?

TL;DR

This paper explores how anisotropic primordial gravitational waves could influence photon polarization through graviton-photon scattering, offering a potential new method to detect such anisotropies via CMB polarization, despite small expected effects.

Contribution

It derives general equations for photon polarization transfer due to graviton scattering and applies them to primordial anisotropic gravitons, proposing a novel detection approach.

Findings

Photon polarization modes couple in the presence of anisotropic gravitons.

Effects on CMB polarization are very small but potentially detectable.

Provides a new theoretical framework for gravitational wave background detection.

Abstract

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.