[Paper Review] Probing Parity-Violation with the Four-Point Correlation Function of BOSS Galaxies

Oliver H. E. Philcox|arXiv (Cornell University)|Jun 9, 2022

Astronomy and Astrophysical Research4 citations

TL;DR

This paper presents a blind analysis of the parity-odd four-point correlation function (4PCF) in the BOSS CMASS galaxy survey to probe parity-violating physics in the early Universe. Using advanced estimators and non-parametric statistical tests, it reports a 2.9σ detection (99.6% significance) of parity violation, potentially indicating new physics or systematic effects, and constrains models involving inflaton–gauge field couplings with improved bounds.

ABSTRACT

Parity-violating physics in the early Universe can leave detectable traces in late-time observables. Whilst vector- and tensor-type parity-violation can be observed in the $B$-modes of the cosmic microwave background, scalar-type signatures are visible only in the four-point correlation function (4PCF) and beyond. This work presents a blind test for parity-violation in the 4PCF of the BOSS CMASS sample, considering galaxy separations in the range $[20,160]h^{-1}\mathrm{Mpc}$. The parity-odd 4PCF contains no contributions from standard $Λ$CDM physics and can be efficiently measured using recently developed estimators. Data are analyzed using both a non-parametric rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a compressed $χ^2$ analysis, with the former avoiding the assumption of a Gaussian likelihood. These find similar results, with the rank test giving a detection probability of $99.6\%$ ($2.9σ$). This provides significant evidence for parity-violation, either from cosmological sources or systematics. We perform a number of systematic tests: although these do not reveal any observational artefacts, we cannot exclude the possibility that our detection is caused by the simulations not faithfully representing the statistical properties of the BOSS data. Our measurements can be used to constrain physical models of parity-violation. As an example, we consider a coupling between the inflaton and a $U(1)$ gauge field and place bounds on the latter's energy density, which are several orders of magnitude stronger than those previously reported. Upcoming probes such as DESI and Euclid will reveal whether our detection of parity-violation is due to new physics, and strengthen the bounds on a variety of models.

Motivation & Objective

• To test for parity-violating signals in the large-scale structure using the four-point correlation function (4PCF), which is sensitive to scalar-type parity violation not detectable in lower-order statistics.
• To develop and apply a robust statistical framework—using non-parametric rank tests and compressed χ² analysis—without assuming Gaussian likelihoods, to avoid biases in significance estimation.
• To assess whether the observed signal arises from cosmological physics beyond ΛCDM or from systematic effects in data or simulations.
• To constrain physical models of parity violation, particularly those involving a coupling between the inflaton and a U(1) gauge field, using the observed 4PCF signal.
• To provide a foundation for upcoming surveys like DESI and Euclid to confirm or rule out the detection as evidence of new physics.

Proposed method

• Utilizes the parity-odd 4PCF as a probe of scalar-type parity violation, which is absent in standard ΛCDM but can be sourced by physics such as Chern-Simons coupling or primordial vector fields.
• Employs a recently developed O(N²) algorithm to compute the 4PCF efficiently from the BOSS CMASS galaxy sample over scales [20, 160] h⁻¹ Mpc.
• Applies two independent statistical tests: a non-parametric rank test comparing the observed 4PCF to those from realistic simulations, and a compressed χ² test, both avoiding Gaussian likelihood assumptions.
• Projects the 4PCF into an angular harmonic basis using isotropic basis functions and Bessel function integrals to decouple spatial correlations and enable efficient computation.
• Derives analytical expressions for the 4PCF in the presence of a Chern-Simons-type interaction, involving Wigner 9-j symbols and coupling matrices from five-coordinate isotropic basis functions.
• Performs systematic checks on data and simulation fidelity to assess whether the signal could be due to simulation inaccuracies or observational systematics.

Experimental results

Research questions

• RQ1 Is there a statistically significant signal of parity violation in the four-point correlation function of BOSS CMASS galaxies on scales [20, 160] h⁻¹ Mpc?
• RQ2 Can the observed signal be explained by standard ΛCDM physics, or does it point to new physics such as a coupling between the inflaton and a U(1) gauge field?
• RQ3 Are the observed 4PCF measurements consistent with those predicted by simulations, or do they indicate a failure of simulation fidelity in capturing the true statistical properties of the data?
• RQ4 What constraints can be placed on the energy density of a primordial U(1) gauge field based on the observed 4PCF signal?
• RQ5 Will upcoming surveys like DESI and Euclid be able to confirm or rule out the observed 2.9σ signal as evidence of new physics?

Key findings

• A 2.9σ detection of parity violation is found in the 4PCF of the BOSS CMASS sample, with a detection probability of 99.6% using the non-parametric rank test.
• The compressed χ² analysis yields consistent results, supporting the robustness of the detection across different statistical frameworks.
• Systematic tests do not identify observational systematics as the source of the signal, though the simulations may not fully capture the statistical properties of the data, leaving open the possibility of simulation-related biases.
• The observed 4PCF signal allows for constraints on the energy density of a primordial U(1) gauge field, improving previous bounds by several orders of magnitude.
• The signal is consistent with a parity-violating interaction such as a Chern-Simons coupling between the inflaton and a gauge field, suggesting a potential origin in early-universe physics.
• Upcoming surveys such as DESI and Euclid are expected to provide higher-significance tests of this signal and further constrain a wide range of parity-violating models.