Measuring Polarization In Cosmic Microwave Background

TL;DR

This work analyzes measuring polarization in the CMB, focusing on scalar-perturbation-induced polarization and its Fourier-domain treatment. It develops optimal 2-point estimators for $C_{Tl}$, $C_{Pl}$, and $C_{Cl}$, and demonstrates how polarization data—particularly the $E$/$B$ decomposition and cross-spectra—can break parameter degeneracies and probe reionization and tensor modes. It also discusses foreground removal strategies, tensor polarization, and model predictions, showing that satellite missions could achieve unambiguous polarization detections and provide powerful tests of early-universe physics. Overall, the paper provides a comprehensive framework for extracting cosmological information from CMB polarization, including robust techniques to separate signal from foregrounds and noise.

Abstract

Polarization induced by cosmological scalar perturbations leads to a typical anisotropy pattern, which can best be analyzed in Fourier domain. This allows one to unambiguously distinguish cosmological signal of polarization from other foregrounds and systematics, as well as from polarization induced by non-scalar perturbations. The precision with which polarization and cross-correlation power spectra can be determined is limited by cosmic variance, noise and foreground residuals. Choice of estimator can significantly improve our capability of extracting cosmological signal and in the noise dominated limit the optimal power spectrum estimator reduces the variance by a factor of two compared to the simplest estimator. If foreground residuals are important then a different estimator can be used, which eliminates systematic effects from foregrounds so that no further foreground subtraction is needed. A particular combination of Stokes $Q$ and $U$ parameters vanishes for scalar induced polarization, thereby allowing an unambiguous determination of tensor modes. Theoretical predictions of polarization in standard models show that one typically expects a signal at the level of 5-10$μ$K on small angular scales and around 1$μ$K on large scales ($l<200$). Satellite missions should be able to reach sensitivities needed for an unambiguous detection of polarization, which would help to break the degeneracies in the determination of some of the cosmological parameters.

Figures (2)

• Figure 1: Power spectra of polarization (a), temperature-polarization cross correlation (b), temperature (c) and correlation coefficient (d). The models are standard CDM (solid curve), open CDM (dotted curve) and reionized standard CDM with optical depth of 0.2 (dashed curve).
• Figure 2: Variance in polarization (a) and cross-correlation power spectrum (b) for a satellite with noise characteristic $w_P=w_T/2$. We assumed 50% sky coverage and $0.3^\circ$ degree beam ($0.2^\circ$ in the most optimistic case). The spectra were averaged over a 20% band in $l$ and the bands shown are one standard deviation above and below the underlying model, taken to be COBE normalized standard CDM.