Circular polarization in a spherical basis

Abstract

Circular polarization of the cosmic microwave background (CMB) arises in the standard cosmological model from Faraday conversion of the linear polarization generated at the surface of last scatter by various sources of birefringence along the line of sight. If the sources of birefringence are generated at linear order in primordial density perturbations the principal axes of the index-of-refraction tensor are determined by gradients of the primordial density field. Since linear polarization at the surface of last scatter is generated at linear order in density perturbations, the circular polarization thus arises at second order in primordial perturbations. Here, we re-visit the calculation of the circular polarization using the total-angular-momentum formalism, which allows for some simplifications in the calculation of the angular power spectrum of the circular polarization---especially for the dominant photon-photon scattering contribution---and also provides some new intuition.

6 pages

References in corpus (5)

• De-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism
• Carbon Monoxide Intensity Mapping at Moderate Redshifts
• Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields
• Generation of circular polarization in CMB radiation via nonlinear photon-photon interaction
• Wigner-Eckart theorem in cosmology: Bispectra for total-angular-momentum waves

Cited by in corpus (14)

• Pulsar-timing arrays, astrometry, and gravitational waves
• Two-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: A Measurement of Circular Polarization at 40 GHz
• CMB circular and B-mode polarization from new interactions
• Circular polarization of the cosmic microwave background from vector and tensor perturbations
• Relations between angular and Cartesian orientational expansions
• Chiral photons from chiral gravitational waves
• CMB $V$ modes from photon-photon forward scattering revisited
• Physics Beyond The Standard Model with Circular Polarization in the CMB and CMB-21cm Cross-Correlation
• Generation of Circular Polarization of CMB via Polarized Compton Scattering
• CMB polarization as a tool to constrain the optical properties of the Universe
• Circularly Polarized EM Radiation from GW Binary Sources
• Primordial Circular Polarization in the Cosmic Microwave Background
• Dipolar dark matter and CMB B-mode polarization
• Secondary CMB anisotropies from magnetized halos --I: Power spectra of the Faraday rotation angle and conversion rate