CMB V modes from photon-photon forward scattering revisited

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 ≈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.

Non-Markovian open quantum system approach to the early universe: I. Damping of gravitational waves by matter

“…However, to study the dynamics of the systems on an expanding background we must use other techniques. Here, we take the approach of the so-called QBE instead [8][9][10][11][12][13] (see [54][55][56][57][58][59][60][61] for the application of OQS to the inflation models). We aim to apply our non-Markovian formalism to a system of soft gravitons coupled to a background of decoupled ultra-relativistic fermions.…”

“…To find the quantum Boltzmann equation, we start with the time evolution of the number operator associated with the system's degrees of freedom given in the following form [8][9][10][11][12][13] d dt…”

“…The formalism of the Quantum Boltzmann Equation (QBE) was initially developed to study the time evolution of the intensity and the polarization of the Cosmic Microwave Background (CMB) photons [8][9][10][11][12]. One way to formulate such a quantum kinetic equation is to use the open quantum system approach.…”

“…One way to formulate such a quantum kinetic equation is to use the open quantum system approach. Starting from a master equation describing the CMB photon density matrix dynamics, applying the Born-Markov approximation, and finally, after taking the operator expectation values, the QBE arises [8][9][10][11][12][13]. The QBE is an accurate tool to extract the effects of microscopic interactions on the macroscopic properties of the intensity and the polarization of the CMB radiation.…”

Probing Virtual ALPs by Precision Phase Measurements: Time-Varying Magnetic Field Background

“…The inhomogeneity of the external magnetic field caused a momentum transfer to the vertex of the interaction. This process was well described by an effective interaction Hamiltonian that was defined in terms of the second-order S-matrix operator [28][29][30][31][32]. We chose a spatially periodic magnetic field B(x) ∝ B 0 cos(x/ ) along the cavity axis (x-direction) with the wavelength .…”