What is the B mode in CMB polarization?

TL;DR

This paper explains the B mode in CMB polarization as a key signature of primordial gravitational waves, detailing its mathematical formalism on spherical surfaces and its significance for inflation theory.

Contribution

It generalizes the formalism of polarization decomposition from plane to spherical surfaces, connecting scalar functions to vector and tensor spherical harmonics.

Findings

B mode as a signature of primordial gravitational waves

Formalism extended to spherical surfaces using cartesian coordinates

Analysis of global data with vector and tensor spherical harmonics

Abstract

A linear polarization field on a surface is expressed in terms of scalar functions, providing an invariant separation into two components; one of these is the B mode, important as a signature of primordial gravitational waves, which would lend support to the inflation hypothesis. The case of a plane already exhibits the key ideas, including the formal analogy with a vector field decomposed into gradient plus curl, with the B mode like the latter. The formalism is generalized to a spherical surface using cartesian coordinates. Analysis of global data provides a path to vector and tensor spherical harmonics.