Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies

Abstract: A tetrahedron is the simplest shape that cannot be rotated into its mirror image in 3D. The 4-Point Correlation Function (4PCF), which quantifies excess clustering of quartets of galaxies over random, is the lowest-order statistic sensitive to parity violation. Each galaxy defines one vertex of the tetrahedron. Parity-odd modes of the 4PCF probe an imbalance between tetrahedra and their mirror images. We measure these modes from the largest currently available spectroscopic samples, the 280,067 Luminous Red Galaxies (LRGs) of the Baryon Oscillation Spectroscopic Survey (BOSS) DR12 LOWZ ($\bar{z} = 0.32$) and the 803,112 LRGS of BOSS DR12 CMASS ($\bar{z} = 0.57$). In LOWZ we find $3.1\sigma$ evidence for a non-zero parity-odd 4PCF, and in CMASS we detect a parity-odd 4PCF at $7.1\sigma$. Gravitational evolution alone does not produce this effect; parity-breaking in LSS, if cosmological in origin, must stem from the epoch of inflation. We have explored many sources of systematic error and found none that can produce a spurious parity-odd \textit{signal} sufficient to explain our result. Underestimation of the \textit{noise} could also lead to a spurious detection. Our reported significances presume that the mock catalogs used to calculate the covariance sufficiently capture the covariance of the true data. We have performed numerous tests to explore this issue. The odd-parity 4PCF opens a new avenue for probing new forces during the epoch of inflation with 3D LSS; such exploration is timely given large upcoming spectroscopic samples such as DESI and Euclid.

• The paper demonstrates statistically significant detection of parity-odd modes in the 4PCF with 7.1σ for CMASS and 3.1σ for LOWZ samples.
• The paper employs rigorous analytic, compressed, and mock covariance analyses to account for survey geometry and mitigate systematic errors.
• The results suggest inflationary origins for the detected signals, opening new avenues for exploration in upcoming surveys like DESI and Euclid.

Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies

This paper addresses the measurement of parity-odd modes in the galaxy distribution from the BOSS DR12 CMASS and LOWZ samples. The 4-Point Correlation Function (4PCF) is utilized to explore these modes, which are sensitive to parity violation and can potentially uncover novel aspects of early-Universe physics.

The authors analyze substantial spectroscopic galaxy samples: 280,067 LRGs from the LOWZ and 803,112 LRGs from the CMASS samples. They find compelling evidence for parity-odd 4PCF modes, with significances at $3.1\sigma$ for LOWZ and $7.1\sigma$ for CMASS. This detection, purportedly unaccounted for by gravitational evolution, posits an origination from the inflationary epoch if considered cosmological. It foregrounds the emergence of new physics, potentially probing forces active during the early universe.

The methodology is meticulous in its use of large data samples and rigorous in testing for systematic errors that could mimic parity-violation. Several algorithms compute the 4PCF while accounting for survey geometry and systematic errors. In analyzing systematic effects, the authors find no conclusive evidence that artifacts or procedures could entirely account for the detected signal.

To ensure robust results, they perform multiple analytic approaches:

1. Analytic Covariance Approach: This uses a Gaussian Random Field-derived covariance matrix, calibrated through mock catalogs adjusted for volume and density.
2. Compressed Analysis: Here, the dimensionality is reduced to enable the manageable inversion of the covariance matrix derived from the mocks. It ensures the covariance estimation is less susceptible to marginal components that might skew results.
3. Mock Covariance Analysis: Reduced to include a fewer number of channels (lower $\ell_{\rm max}$), this analysis relies entirely on mock-derived covariances for validation through a direct inversion process.

In examining the cosmological and observational implications, their research invites reinterpretation of data from spectroscopic surveys like DESI and Euclid, which may further illuminate parity phenomena or confirm the inflationary theories hinted at in this work. A notable outcome is the opportunity the odd-parity 4PCF presents in exploring forces or fields possibly active during the epoch of cosmic inflation, such as Chern-Simons couplings that may interact with primordial gravitational waves or scalar fields.

Ultimately, this study expands the toolkit for cosmological examination, suggesting a new field of research into the potential parity violation in large-scale structures. Future works, possibly leveraging larger datasets from forthcoming surveys, may unveil more about the fundamental architecture of the cosmos and the forces shaping it.