[Paper Review] A Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies

R. N. Cahn, Zachary Slepian+1 more|arXiv (Cornell University)|Oct 20, 2021

Cosmology and Gravitation Theories22 references4 citations

TL;DR

This paper proposes a novel test for cosmological parity violation using the 3D galaxy 4-Point Correlation Function (4PCF), leveraging the fact that tetrahedral configurations in 3D cannot be superimposed on their mirror images, making them sensitive to parity-violating physics. The method uses a basis of isotropic functions to make the 4PCF computationally feasible and demonstrates that such a signal would indicate primordial non-Gaussianity and new physics beyond the Standard Model.

ABSTRACT

We show that the galaxy 4-Point Correlation Function (4PCF) can test for cosmological parity violation. The detection of cosmological parity violation would reflect previously unknown forces present at the earliest moments of the Universe. Recent developments both in rapidly evaluating galaxy $N$-Point Correlation Functions (NPCFs) and in determining the corresponding covariance matrices make the search for parity violation in the 4PCF possible in current and upcoming surveys such as those undertaken by Dark Energy Spectroscopic Instrument (DESI), the $Euclid$ satellite, and the Vera C. Rubin Observatory (VRO).

Motivation & Objective

• To develop a model-free test for cosmological parity violation using the 3D distribution of galaxies.
• To detect parity-violating signals in large-scale structure that could indicate new fundamental forces from the early Universe.
• To enable robust analysis of 4PCF in upcoming surveys like DESI, Euclid, and Vera C. Rubin Observatory.
• To address computational and systematic challenges in measuring the 4PCF and its covariance matrix.
• To provide a framework for testing parity violation in higher-order correlation functions beyond the 4PCF.

Proposed method

• The 4PCF is decomposed into parity-conserving and parity-violating components using a basis of isotropic functions parameterized by three radial bins and three angular indices.
• The method relies on the geometric property that in 3D, a tetrahedron and its mirror image cannot be superimposed, making the 4PCF sensitive to parity violation.
• A Gaussian random field covariance template is analytically derived and calibrated with mock catalogs to ensure numerical stability and positive semi-definiteness.
• The analysis accounts for survey geometry using random catalogs and a redshift-dependent selection function inferred from data to avoid spurious parity violation.
• Systematic effects from fiber-positioner limitations in spectroscopic surveys (e.g., DESI) are acknowledged as requiring future correction methods for the 4PCF.
• The approach is extendable to 5-point and higher correlation functions using algebraic structures from prior work.

Experimental results

Research questions

• RQ1 Can the 3D galaxy 4-Point Correlation Function detect cosmological parity violation in large-scale structure?
• RQ2 What is the computational feasibility of measuring parity-violating components of the 4PCF in current and upcoming surveys?
• RQ3 How can the covariance matrix of the 4PCF be reliably estimated to distinguish signal from noise?
• RQ4 What systematic effects in spectroscopic surveys could mimic or obscure a parity-violating signal in the 4PCF?
• RQ5 Can the 4PCF serve as a probe of primordial non-Gaussianity and new physics beyond the Standard Model?

Key findings

• The 4PCF is sensitive to parity violation because tetrahedral configurations in 3D are chiral and cannot be superimposed on their mirror images.
• Parity-violating signals in the 4PCF would indicate primordial non-Gaussianity, as a purely Gaussian random field produces only parity-conserving 4PCF components.
• The method uses a basis of isotropic functions labeled by three radial bins and three angular indices, enabling computationally feasible analysis of the 4PCF.
• An analytical covariance matrix template derived under Gaussian assumptions provides a stable, invertible foundation that can be calibrated with mock catalogs.
• Current and upcoming surveys such as DESI, Euclid, and the Vera C. Rubin Observatory are expected to provide sufficient data for stringent tests of parity violation.
• The framework is generalizable to higher-order correlation functions, such as the 5PCF, using established algebraic structures.