All-sky analysis of polarization in the microwave background

Abstract

Using the formalism of spin-weighted functions we present an all-sky analysis of polarization in the Cosmic Microwave Background (CMB). Linear polarization is a second-rank symmetric and traceless tensor, which can be decomposed on a sphere into spin ±2 spherical harmonics. These are the analog of the spherical harmonics used in the temperature maps and obey the same completeness and orthogonality relations. We show that there exist two linear combinations of spin ±2 multipole moments which have opposite parities and can be used to fully characterize the statistical properties of polarization in the CMB. Magnetic-type parity combination does not receieve contributions from scalar modes and does not cross-correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize statistical properties of CMB. We present their explicit expressions for scalar and tensor modes in the form of line of sight integral solution and numerically evaluate them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. A method to generate and analyze all sky maps of temperature and polarization is given and the optimal estimators for various power spectra and their corresponding variances are discussed.98.70.V, 98.80.C

Inflation and String Theory

“…First of all, unlike the Stokes parameters, the parameters E and B are independent of the choice of coordinates. More importantly, symmetry forbids the generation of B-modes by scalar fluctuations [77,78]. B-modes are therefore a crucial signature of the presence of tensor (or vector) fluctuations.…”

Observational probes of cosmic acceleration

“…Formulae such as (73) and (77) may be generalized to the full sky, as was first done for CMB polarization (Kamionkowski et al, 1997;Zaldarriaga and Seljak, 1997), but for cosmic shear most applications involve small angular scales where the flat-sky approximation suffices. 36 Having built the formalism to describe the statistics of weak lensing, we can now consider the proposed ways of using it to measure cosmology.…”

Correlation Functions of CMB Anisotropy and Polarization

“…It has been discussed how to construct the optimal estimators for the power spectra corrected for noise bias, and their corresponding variances from the all-sky map [14,15,20]. To estimate the level of signal and noise, we hereby give an alternative real-space analysis, evaluating the ensemble means and variances of the full-sky averaged correlation function estimators for the MAP and Planck configurations, i.e.…”