# Parity-Odd Power Spectra: Concise Statistics for Cosmological Parity Violation

**Authors:** Drew Jamieson, Angelo Caravano, Jiamin Hou, Zachary Slepian, Eiichiro Komatsu  
**arXiv:** [2406.15683](https://arxiv.org/abs/2406.15683)  
**Date:** 2024-06-21  
**Summary page:** https://www.summarizepaper.com/fr/paper/2406.15683v1/

## Abstract

We introduce the Parity-Odd Power (POP) spectra, a novel set of observables for probing parity violation in cosmological $N$-point statistics. POP spectra are derived from composite fields obtained by applying nonlinear transformations, involving also gradients, curls, and filtering functions, to a scalar field. This compresses the parity-odd trispectrum into a power spectrum. These new statistics offer several advantages: they are computationally fast to construct, estimating their covariance is less demanding compared to estimating that of the full parity-odd trispectrum, and they are simple to model theoretically. We measure the POP spectra on simulations of a scalar field with a specific parity-odd trispectrum shape. We compare these measurements to semi-analytic theoretical calculations and find agreement. We also explore extensions and generalizations of these parity-odd observables.