A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit

TL;DR

This paper derives a consistency relation linking large-scale temperature perturbations with small-scale B-mode polarization, aiding in distinguishing primordial signals from galactic foregrounds in CMB observations.

Contribution

It introduces a new theoretical relation connecting the squeezed limit of the TBB three-point function with the B-mode power spectrum, useful for primordial signal identification.

Findings

Derived a relation connecting TBB three-point function with B-mode power spectrum.

Provides a method to differentiate primordial B-modes from galactic dust contamination.

Enhances the analysis toolkit for CMB polarization studies.

Abstract

A large-scale temperature perturbation has a non-zero correlation with the power spectrum of B-modes of cosmological origin on short scales while the corresponding correlation is expected to be zero for B-modes sourced by galactic foregrounds. We thus compute the squeezed limit of a three-point function in which one correlates the temperature fluctuations at large scales with two polarization modes at small scales. In the particular case of the B-mode polarization we obtain a relation that connects the squeezed limit of the $TBB$ three-point function with the cosmological B-mode power spectrum, which can be used as a consistency relation. This could in principle help to distinguish a primordial signal from that induced by inter-stellar dust.