Odd-Parity Bipolar Spherical Harmonics

TL;DR

This paper introduces odd-parity bipolar spherical harmonics (BiPoSHs) as a new formalism to detect departures from statistical isotropy and Gaussianity in the CMB, with potential applications in identifying parity-breaking physics like chiral gravitational waves.

Contribution

It extends the BiPoSH formalism to include odd-parity modes and explores their cosmological applications, including lensing effects and detection of parity-breaking phenomena.

Findings

Odd-parity BiPoSHs can be induced by lensing from gravitational waves.

Cross-correlating opposite parity BiPoSH modes with CMB polarization can probe parity-breaking physics.

Expected detection signals for parity-breaking effects are modest.

Abstract

Bipolar spherical harmonics (BiPoSHs) provide a general formalism for quantifying departures in the cosmic microwave background (CMB) from statistical isotropy (SI) and from Gaussianity. However, prior work has focused only on BiPoSHs with even parity. Here we show that there is another set of BiPoSHs with odd parity, and we explore their cosmological applications. We describe systematic artifacts in a CMB map that could be sought by measurement of these odd-parity BiPoSH modes. These BiPoSH modes may also be produced cosmologically through lensing by gravitational waves (GWs), among other sources. We derive expressions for the BiPoSH modes induced by the weak lensing of both scalar and tensor perturbations. We then investigate the possibility of detecting parity-breaking physics, such as chiral GWs, by cross-correlating opposite parity BiPoSH modes with multipole moments of the CMB polarization. We find that the expected signal-to-noise of such a detection is modest.