Can the CMB be Odd? Effect of a Parity-Violating Matter 4-Point Function on the Low-$\ell$ CMB Trispectrum

TL;DR

This paper investigates how parity violation in large-scale structure could influence the low-$$ CMB trispectrum, finding that non-detection does not rule out PV signals in matter correlations.

Contribution

It provides a theoretical analysis of the sensitivity of the CMB trispectrum to parity violation in large-scale structure, considering a scale-limited PV model.

Findings

Odd CMB trispectrum suppressed by about 1% relative to matter 4PCF

Non-detection of PV in CMB does not exclude PV in LSS 4PCF

Focus on Sachs-Wolfe term at low multipoles

Abstract

Here we explore from a theoretical perspective the sensitivity of the primary CMB anisotropy trispectrum to parity violation (PV) in large-scale structure (LSS). We focus on the Sachs-Wolfe term, which dominates at $\ell < 40$, after which the Doppler term takes over. We consider a model where the PV is only present out to some maximal scale $R$ of order a few hundred Mpc/$h$, consistent with what recent LSS 4PCF measurements seem to indicate. We find that the odd CMB trispectrum must be suppressed by at least one factor of $R/\chi_*$$\simeq$1\%, with $\chi_*$ the distance to last scattering, relative to the input matter 4PCF. Thus, a non-detection of PV in the CMB trispectrum is \textit{not necessarily inconsistent} with a genuine detection of PV in the LSS 4PCF.