Testing parity with composite-field spectra of BOSS and DESI luminous red galaxies

Abstract: Detection of parity violation on cosmological scales would have profound implications for fundamental physics. Motivated in part by recent measurements of parity-odd four-point correlation functions in BOSS and DESI luminous red galaxy samples, which probe parity violation in the scalar sector, we present the first measurement of parity-odd kurto spectra in spectroscopic galaxy survey data. We analyse two composite-field spectra, $\mathcal{P}<em>{2\times2}$ (vector--pseudo-vector) and $\mathcal{P}</em>{3\times1}$ (scalar--pseudo-scalar). Compared with parity-odd four-point correlation function analyses, the kurto-spectrum formalism performs physically motivated compression on the trispectrum into a substantially lower-dimensional data vector, allowing direct estimation of covariance matrices from mock catalogues and reducing sensitivity to covariance-modelling systematics. Using null-hypothesis $χ<sup>2$ tests and cross-patch consistency checks, we find no evidence for a cosmological parity-violating signal in either survey. We examine the impact of the adopted mock catalogues and find that the high-fidelity mocks provide a better match to the data of both surveys than the approximate mocks. The DESI DR1 measurements exhibit a scatter smaller than that of BOSS DR12 by about a factor of four, consistent with the improved statistical precision expected from the higher tracer number density. Future DESI data releases, with larger volume and number density, together with larger suites of high-fidelity mocks, can enable significantly sharper tests of parity violation using kurto spectra.