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The Odd-Parity CMB Bispectrum

Marc Kamionkowski, Tarun Souradeep

TL;DR

This work points out and characterizes a previously unexplored class of odd-parity CMB bispectra, which cannot be produced by a parity-invariant 3D density field and can arise from parity-violating processes such as lensing by a chiral gravitational-wave background or cosmological birefringence (leading to configurations with $l_1+l_2+l_3$ odd). It develops the formalism to measure these bispectra, including reduced and rotationally invariant representations and a modified estimator using $G_{l_1l_2l_3}$ to handle odd configurations, enabling a potential null test of standard even-parity analyses and a probe for new physics, albeit with expected small amplitudes.

Abstract

Measurement of the cosmic microwave background (CMB) bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is a odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data.

The Odd-Parity CMB Bispectrum

TL;DR

This work points out and characterizes a previously unexplored class of odd-parity CMB bispectra, which cannot be produced by a parity-invariant 3D density field and can arise from parity-violating processes such as lensing by a chiral gravitational-wave background or cosmological birefringence (leading to configurations with odd). It develops the formalism to measure these bispectra, including reduced and rotationally invariant representations and a modified estimator using to handle odd configurations, enabling a potential null test of standard even-parity analyses and a probe for new physics, albeit with expected small amplitudes.

Abstract

Measurement of the cosmic microwave background (CMB) bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is a odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data.

Paper Structure

This paper contains 1 section, 11 equations, 1 figure.

Table of Contents

  1. Introduction

Figures (1)

  • Figure 1: Here we plot two Fourier triangles with $l_1<l_2<l_3$ on a small patch of sky. The two have opposite handedness: in (a) the cross product $\vec{l}_1\times \vec{l}_2$ comes out of the page, while in (b) the cross product goes into the page. The even-parity bispectrum (that with $l_1+l_2+l_3=$even) weights both of these triangles similarly. The odd-parity bispectrum (configurations with $l_1+l_2+l_3$=odd) takes on different signs for the two different triangles.