Searching for parity violation in SDSS DR16 Lyman-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math> forest data

The four-point correlation function is the lowest order correlation function for scalar fields that can be used to probe statistical parity invariance in an isotropic universe. There are intriguing claims of detection of parity violation in the 4-point function of BOSS galaxy clustering data. We apply the same estimator to the public SDSS Data Release 16 Lyman-$\ensuremath{\alpha}$ forest data. Lyman-$\ensuremath{\alpha}$ forest data probes a different redshift range and is sensitive to a different density regime using a completely different technique. A detection would therefore be a strong indication of new physics. We identify an accurate covariance matrix as a crucial impediment to performing this measurement accurately, consistent with existing literature on galaxy 4-point function. We discuss several approaches to estimating the covariance matrix, several of which produce spurious detection. Using a robust, but very suboptimal, covariance matrix derived from subsample bootstrapping, we find no evidence for parity violation.