Over the course of the project, substantial progress was made in developing, testing, and applying higher-order statistical tools to cosmological data, including algorithmic innovation, theoretical modelling, and observational applications.
Results and Exploitation:
1: Develop tools for robust analysis for higher-order functions of galaxy distributions
The primary objective of this package was to develop higher-order statistics in configuration space, focusing on 3- and 4-point correlation functions, including modeling, covariance matrix, and systematics. Key accomplishments include:
• Development of N-point Function Algorithm: Contributed to an N-point function algorithm designed to measure N-point functions up to an arbitrarily high N [Philcox, Slepian, Hou+, 2021, MNRAS 509, 2457].
• GPU Acceleration: Advised a student on enhancing the N-point function algorithm with GPU acceleration [Hix, Hou, Slepian, 2023, AAS Meeting Abstracts 55, 306.10].
• Fast Fourier Transforms: Co-advised a student on utilizing fast Fourier transforms for 3- and 4-point correlation functions [Sunseri (incl. Hou), 2023, RASTI 2, 62-77].
• Analytic Covariance Matrix: Calculated an analytic template for the covariance matrix for any arbitrary N-point function in configuration space [Hou et al., 2022, PRD 106, 043515], addressing the computational expense traditionally required for quantifying error bars.
• Modeling Higher-Order Statistics: Co-advised a student on modeling the 4-point function for galaxy clustering [Ortolá-Leonard, Slepian, Hou, 2024, arXiv:2402.15510].
• Investigate the signature of baryon acoustic oscillations (BAO) in parity-violating simulations [Hou et al, 2024, arXiv:2410.05230].
2: Provide a Complementary Treatment of the Full N-Point Statistics
The goal of this package was to develop compressed estimators that offer advantages of speed and reduced dimensionality compared to conventional N-point statistics. Key accomplishments include:
• Skew Spectra: Developed skew spectra as a compressed 3-point statistic and applied it to simulations for dark matter halos and galaxy catalogs, demonstrating its cosmological information content [Hou et al. 2023 JCAP 2023, 045].
• Machine-learning with skew spectra: Construct a suite of synthetic galaxy catalogs, using them to train the skew spectra and employing machine learning approaches to quantify cosmological information content in real galaxy data [Hou et al. 2024 PRD 109, 103528].
• Parity-Odd Power Spectrum (POP): Developed a compressed 4-point estimator sensitive to parity violation in 3D fields [Jamieson, Caravano, Hou, Slepian, Komatsu, 2024, accepted by MNRAS].
• Co-lead a working group on higher-order clustering within Dark Energy Spectroscopic Instrument
3: Use Higher-Order Statistics to Test Models Beyond the LCDM Scenario
This package aimed to explore beyond-standard cosmological models, including those involving modified gravity, parity violation, and deviations from single-field slow-roll inflation. Key accomplishments include:
• Review on Modified Gravity: Led a comprehensive review paper on the observational aspects of modified gravity, consolidating current constraints and methodologies, and providing a roadmap for future studies [Hou et al. 2023 Universe 9, 302].
• Testing Parity Violation: Proposed a novel approach to test parity violation at cosmological scales using the galaxy 4-point function [Cahn, Slepian, Hou, 2023, PRL 130, 201002]; applied it to real data, detecting potential parity-violating signature [Hou, Slepian, Cahn, 2023, MNRAS 522, 5701–5739].
• Axion Inflation: Co-advised a PhD student on computing the 4-point correlation function for the axion inflationary model [Reinhard, Slepian, Hou, Grecco, 2024, arXiv:2412.16037].
• First 4PCF Measurement on MHD simulation: Co-advised a Bachelor student on the 4-point correlation function measurement of the magnetohydrodynamic simulation [Williamson, Sunseri, Slepian, Hou, Grecco, 2024, arXiv:2412.03967].
• CMB lensing: apply the 4PCF to the CMB lensing in the presence of primordial parity-violating mechanism [Grecco, Slepian, Hou, 2025, arXiv:2505.15789v1].
Dissemination:
Results have been disseminated through peer-reviewed publications, 14 talks (including 9 invited and 3 colloquia), dedicated workshops, and leadership roles in DESI. Tools and pipelines have been shared via student mentorship and collaborative publications. The work on cosmological parity violation received media coverage, bringing these developments to a broader audience.
