[Paper Review] The Cosmic Microwave Background and Its Polarization

A. de Oliveira‐Costa|arXiv (Cornell University)|Jun 16, 2004

Cosmology and Gravitation Theories3 citations

TL;DR

This paper reviews the physics and observational status of cosmic microwave background (CMB) polarization, emphasizing its role in probing inflationary gravitational waves and the reionization epoch. It details how Thomson scattering generates E- and B-mode polarization, links these to cosmological parameters, and evaluates Galactic foregrounds—especially synchrotron and dust emission—that limit large-scale CMB polarization measurements.

ABSTRACT

The DASI discovery of CMB polarization, confirmed by WMAP, has opened a new chapter in cosmology. Most of the useful information about inflationary gravitational waves and reionization is on large angular scales where Galactic foreground contamination is the worst. The goal of the present review is to provide the state-of-the-art of the CMB polarization from a practical point of view, connecting real-world data to physical models. We present the physics of this polarized phenomena and illustrate how it depends of various cosmological parameters for standard adiabatic models. We also present all observational constraints to date and discuss how much we have learned about polarized foregrounds so far from the CMB studies. Finally, we comment on future prospects for the measurement of CMB polarization.

Motivation & Objective

• To provide a comprehensive, practical review of CMB polarization connecting observational data to physical cosmological models.
• To analyze how CMB polarization power spectra (TT, TE, EE, BB, TB, EB) depend on cosmological parameters in standard adiabatic models.
• To assess the impact of Galactic foregrounds—especially synchrotron and dust emission—on CMB polarization measurements.
• To evaluate current observational constraints from DASI and WMAP on CMB polarization power spectra.
• To outline future challenges and prospects for detecting primordial B-modes and gravitational waves via CMB polarization.

Proposed method

• Uses spherical harmonic decomposition of CMB temperature (T) and polarization (E, B) maps to define six angular power spectra: TT, TE, EE, TB, EB, BB.
• Applies the E/B-mode decomposition to separate scalar (E-modes only) from tensor (E and B-modes) and lensing-induced B-mode contributions.
• Employs the correlation coefficient $ r_{\ell} = C^{TE}_{\ell}/\sqrt{C^{T}_{\ell} C^{E}_{\ell}} $ to analyze TE cross-spectrum behavior, avoiding logarithmic scaling issues.
• Analyzes foreground contamination using frequency-dependent models of Galactic synchrotron (E/B equal at 408–820 MHz, with Faraday rotation effects at low frequencies) and dust emission (vibrational and rotational components).
• Reviews observational constraints from DASI and WMAP, particularly WMAP’s E-mode maps for quantifying synchrotron polarization at 22–90 GHz.
• Evaluates the potential of future experiments (e.g., Archeops, B2K) to detect polarized dust emission at 353 GHz and characterize spinning dust emission (Foreground-X).

Experimental results

Research questions

• RQ1 How does CMB polarization arise from Thomson scattering during recombination and reionization, and what determines its amplitude and angular scale dependence?
• RQ2 What is the dependence of CMB polarization power spectra (TT, TE, EE, BB, TB, EB) on cosmological parameters such as optical depth, reionization redshift, and primordial gravitational waves?
• RQ3 To what extent do Galactic foregrounds—especially synchrotron and dust emission—contaminate large-scale CMB polarization measurements, and how do they vary with frequency and angular scale?
• RQ4 What is the current observational status of CMB polarization from DASI and WMAP, and how do these measurements constrain cosmological models?
• RQ5 What are the prospects and challenges for detecting primordial B-modes via CMB polarization, and what improvements in instrumentation and foreground modeling are required?

Key findings

• CMB polarization is generated via Thomson scattering when local radiation quadrupoles exist, primarily at recombination (z ≈ 1100) and during reionization (z ≈ 17), with polarization levels typically 1%–10% of temperature anisotropies.
• E-modes are produced by scalar fluctuations and dominate on small to intermediate scales; B-modes arise from tensor modes (primordial gravitational waves) and lensing, with $ C^{B}_{\ell} = 0 $ to first order in scalar models.
• The TE cross-spectrum $ C^{TE}_{\ell} $ is negative for about half of the $ \ell $-modes, and the dimensionless correlation coefficient $ r_{\ell} $ provides a more intuitive diagnostic with bounds $ -1 \leq r_{\ell} \leq 1 $.
• Galactic synchrotron emission shows $ E \approx B $ at 408–820 MHz, but Faraday rotation mixes E and B modes at low frequencies ($ \nu \lesssim 10 $ GHz), especially on large angular scales.
• Polarized dust emission at high frequencies (≥100 GHz) is dominated by vibrational dust, while at lower frequencies (15–60 GHz), a rotational dust component (Foreground-X) may contribute, with uncertain polarization levels depending on emission mechanism.
• Archeops detected 4–5% polarized dust emission at 353 GHz, with polarization orientation mostly perpendicular to the Galactic plane, indicating a strong grain alignment mechanism in the interstellar medium.