# 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/en/paper/2406.15683v1/

## Key points

- The observation of weak nuclear parity violation in 1957 showed differentiation between right-handed and left-handed chiralities.
- Recent investigations have provided compelling evidence for cosmological parity violation within the large-scale structure (LSS) of the Universe.
- Studies analyzing the BOSS galaxy four-point correlation function have revealed signs of parity violation with statistical significance reaching up to 7σ.
- The introduction of Parity-Odd Power (POP) spectra offers advantages over traditional methods in probing parity violation on cosmological scales.
- Measurements of POP spectra on simulations demonstrated agreement between observation and prediction, enhancing our understanding of cosmological parity violation.

## Summary

The study of symmetries and their potential violations has played a crucial role in advancing our understanding of the universe in modern physics. One significant discovery was the observation of weak nuclear parity violation in 1957, which showed that the laws of physics differentiate between right-handed and left-handed chiralities. While this violation is well-established on small scales, the question of its existence on cosmological scales remains a topic of ongoing research. Recent investigations utilizing innovative methods have provided compelling evidence for cosmological parity violation within the large-scale structure (LSS) of the Universe. Studies analyzing the BOSS galaxy four-point correlation function have revealed signs of parity violation with statistical significance reaching up to 7σ. This groundbreaking discovery, as reported by Hou et al. (2023b) and Philcox (2022), could have profound implications for our understanding of fundamental physics. To further explore and probe these findings, a novel set of observables known as Parity-Odd Power (POP) spectra has been introduced. These spectra are derived from composite fields created through nonlinear transformations involving gradients, curls, and filtering functions applied to a scalar field. By compressing the parity-odd trispectrum into a power spectrum, POP spectra offer several advantages over traditional methods. They are computationally efficient to construct, require less demanding covariance estimation compared to full trispectra analysis, and are straightforward to model theoretically. In a recent study by Jamieson et al., measurements of POP spectra were conducted on simulations featuring a specific parity-odd trispectrum shape. The results were compared against semi-analytic theoretical calculations, demonstrating agreement between observation and prediction. Additionally, extensions and generalizations of these parity-odd observables were explored to further enhance our understanding of cosmological parity violation. Overall, the development and application of POP spectra represent a significant advancement in probing parity violation in cosmological N-point statistics. As researchers continue to investigate this intriguing phenomenon, these concise statistics offer a valuable tool for unraveling the mysteries surrounding symmetry breaking on cosmic scales.