CMB $V$ modes from photon-photon forward scattering revisited

TL;DR

This paper revisits the generation of circular polarization in the CMB due to photon-photon interactions, resolving previous discrepancies and showing the effect is extremely small, making detection challenging, while also proposing a general method for studying such effects.

Contribution

It provides a unified approach to calculate CMB $V$ modes from photon-photon scattering and introduces a general framework for potential new physics signatures.

Findings

Circular polarization amplitude is about 8 orders of magnitude smaller than $E$-modes.

The quantum Boltzmann and geometrical approaches yield consistent results.

Generated $V$ modes are extremely challenging to observe.

Abstract

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 $\approx$ 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-1-massive-particle forward scatterings without relying on a specific interaction, which thus represent possible new signatures of physics beyond the Standard Model.