Test parity-violating 4PCF recovery in the matter distribution

Investigate whether the 4-point correlation function auto- and cross-correlation framework recovers the injected parity-violating signal in the Quijote and Quijote-Odd matter distributions, and compare the resulting matter and halo measurements to determine how parity-odd information is reduced before reaching discrete halo tracers.

Background

The study finds no statistically detectable parity-violating signal in the 4-point correlation function of the Quijote-Odd halo catalogs, even though the initial conditions contain a parity-violating primordial trispectrum. Because a prior analysis detected the injected signal in the matter distribution, the absence of a halo-level detection does not establish that the primordial signal is absent; it may instead reflect the effects of halo formation, bias, and discrete sampling.

Applying the same auto- and cross-correlation methodology to the matter field would directly test whether the statistical framework can recover the injected signal when it is present. A comparison between matter and halo measurements could then identify the stage at which parity-odd information is diminished and clarify how primordial parity-violating signatures propagate into the discrete tracers used in galaxy surveys.