Anatomy of Parity-violating Trispectra in Galaxy Surveys

TL;DR

The paper addresses how parity-violating interactions during inflation can leave detectable imprints in the Galaxy via the parity-violating four-point correlation function (4PCF), a signature not produced by standard late-time gravity on large scales. It develops a general pipeline that translates momentum-space trispectra into position-space 4PCFs by leveraging the Schwinger-Keldysh formalism to factorize exchange-type diagrams into radial and angular components, and by using isotropic basis functions to manage angular structure. It systematically builds and analyzes parity-violating templates across canonical local and equilateral shapes, an EFT-like large-mass limit for heavy spin-1 exchange, and full spin-1 and spin-2 exchange models with chemical potential enhancements, providing detailed 4PCF templates and exploring their angular and radial signatures. Applying the framework to BOSS data, the study finds no significant detection of parity violation yet demonstrates a robust method for constraining a broad class of inflationary parity-violating scenarios and outlines promising directions for future surveys and heavier-particle scenarios.

Abstract

Parity-violating interactions are ubiquitous phenomena in particle physics. If they are significant during cosmic inflation, they can leave imprints on primordial perturbations and be observed in correlation functions of galaxy surveys. Importantly, parity-violating signals in the four-point correlation functions (4PCFs) cannot be generated by Einstein gravity in the late universe on large scales, making them unique and powerful probes of high-energy physics during inflation. However, the complex structure of the 4PCF poses challenges in diagnosing the underlying properties of parity-violating interactions from observational data. In this work, we introduce a general framework that provides a streamlined pipeline directly from a particle model in inflation to galaxy 4PCFs in position space. We demonstrate this framework with a series of toy models, effective-field-theory-like models, and full models featuring tree-level exchange-type processes with chemical-potential-induced parity violation. We further showed the detection sensitivity of these models from BOSS data and highlighted potential challenges in data interpretation and model prediction.