Parity-Odd Power Spectra: Concise Statistics for Cosmological Parity Violation

We introduce the Parity-Odd Power (POP) spectra, a novel set of observables for probing parity violation in cosmological $N$-point statistics. POP spectra are derived from composite fields obtained by applying nonlinear transformations, involving also gradients, curls, and filtering functions, to a scalar field. This compresses the parity-odd trispectrum into a power spectrum. These new statistics offer several advantages: they are computationally fast to construct, estimating their covariance is less demanding compared to estimating that of the full parity-odd trispectrum, and they are simple to model theoretically. We measure the POP spectra on simulations of a scalar field with a specific parity-odd trispectrum shape. We compare these measurements to semi-analytic theoretical calculations and find agreement. We also explore extensions and generalizations of these parity-odd observables.