N-point statistics as a bridge between cosmological observations and the underlying physics

Project Information

Cosmo-Bridge

Grant agreement ID: 101025187

DOI

10.3030/101025187

Project closed

EC signature date 14 April 2021

Start date 1 June 2022

End date 31 May 2025

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 264 669,12

EU contribution

€ 264 669,12

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

Periodic Reporting for period 2 - Cosmo-Bridge (N-point statistics as a bridge between cosmological observations and the underlying physics)

Reporting period: 2024-06-01 to 2025-05-31

Summary of the context and overall objectives of the project

The "Cosmic Bridge" project addresses the challenges encountered in data analysis within current and upcoming galaxy surveys, aiming to deepen our understanding of the fundamental nature of the universe. Traditional analysis methods focus primarily on lower-order statistics, which do not fully capture the complexity and richness of the data. The primary goal of the project is to use higher-order statistics to optimally extract information from galaxy surveys. To achieve this, the project focuses on three overall objectives:


1. Develop tools for robust analysis for higher-order functions of galaxy distributions.
2. Provide a complementary treatment of the full N-point statistics.
3. Use higher-order statistics to test models beyond the current standard cosmological model.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The “Cosmic Bridge” project has advanced the field by pushing the boundaries of higher-order statistical analysis and developing innovative tools that go beyond traditional methods. Key progress includes:

• Developed and applied advanced tools for 2-, 3-, and 4-point statistics in configuration space, enhancing the ability to model and extract higher-order statistical information.
• Successfully demonstrated the cosmological information content of skew spectra and parity-odd power spectra through simulations and real data applications.
• Published significant findings on modified gravity and parity violation, contributing to the broader understanding of cosmological models beyond LCDM.
• Achieved outreach and dissemination of research through talks, media coverage, and collaborations, enhancing the visibility and impact of the project.

Expected Results Until the End of the Project:

• The tools and methodologies developed during the project will be applied to the Dark Energy Spectroscopic Instrument (DESI) galaxy data, aiming to extract detailed cosmological information and test models beyond the LCDM scenario.
• The results from the DESI data analysis will be published in leading scientific journals, contributing to the body of knowledge in cosmology and statistical methods.
• Continued dissemination through conferences and public outreach will ensure the findings reach a broad audience, fostering further collaboration and innovation.

Potential Impacts:

• The project’s advancements in higher-order statistics and novel estimators will set new standards in cosmological data analysis, enabling more accurate and comprehensive understanding of the universe.
• The development of advanced computational tools and methodologies can drive innovations in data science, benefiting industries reliant on large-scale data analysis.
• Training students and researchers in these cutting-edge techniques will enhance the skillset of the workforce, contributing to economic growth and technological development.

Parity transformation applied to a tetrahedron formed by a quartet of galaxies.