Parity in Composite-Field Galaxy Correlators

Abstract

Detecting parity violation on cosmological scales would provide a striking clue to new physics. Large-scale structure offers the raw statistical power -- many three-dimensional modes -- to make such tests. However, for scalar observables, like galaxy clustering, the leading parity-sensitive observable is the trispectrum, whose high dimensionality makes the measurement and noise estimation challenging. We present two late-time parity-odd kurto spectra that compress the parity-odd scalar trispectrum into one-dimensional, power-spectrum-like observables. They are built by correlating (i) two appropriately weighted quadratic composite fields, or (ii) a linear and cubic composite field, constructed from dark matter (DM) or galaxy overdensity fields. We develop an FFTLog pipeline for efficient theoretical predictions of the two observables. We then validate the estimators for a specific parity-odd primordial template on perturbative DM field, and on DM and halo fields in full N-body \texttt{Quijote} simulations, with and without parity-odd initial conditions, in real and redshift space. For DM, the variance is dominated by the parity-even contribution -- i.e., the gravitationally induced parity-even trispectrum -- and is efficiently suppressed by phase-matched fiducial subtraction. For halos, discreteness-driven stochasticity dominates and is not appreciably reduced by subtraction; however, optimal weighting and halo-matter cross kurto spectra considerably mitigate this noise and enhance the signal. Using controlled down-sampling of the matter field, we empirically calibrate how the parity-even variance scales with number density and volume, and provide an illustrative forecast for the detectability of parity-odd kurto spectra in a Euclid-like spectroscopic galaxy survey.

Figures (16)

• Figure 1: The EPT $k^2\mathcal{P}_{2\times 2}$ at redshift $z=0$ (a) and $z=1$ (b), with $R_G=5\, \mathrm{Mpc}/h$. Each column corresponds to the five cases, while each row corresponds to each kernel scenario. Note that each row is a new realization of the linear field, thus there is variation in signals even without the second-order fields.
• Figure 2: Real-space matter kurto spectrum $\mathcal{P}_{2\times2}$ at $z=1$ from Quijote snapshots, compared with EPT-field measurements and theory, for $R_G=5\,\mathrm{Mpc}/h$ (figure \ref{['fig:matter_2x2_RG5']}) and $R_G=10\,\mathrm{Mpc}/h$ (figure \ref{['fig:matter_2x2_RG10']}). All spectra are multiplied by $k^{2}$ for visual clarity. In each subfigure, top row shows single realization, while bottom row is the average over 40 realizations. Left panels show QuijoteODD_p (blue dots), matched fiducial simulation (orange solid), EPT tot13 (green dashed), while the right panels show the difference of kurto spectra on ODD_p and fiducial simulations (blue dots), the leading-order $\langle3111\rangle$ contribution on the EPT field (orange dashed). In both panels, the black solid line shows the theoretical prediction of parity-odd signal from eqs. \ref{['eq:P_2x2_type1']} and \ref{['eq:P_2x2_type2']}. The error bars correspond to the diagonal of the full covariance matrix of the $\mathcal{P}_{2\times2}^{\rm PO}$ estimated from 500 fiducial simulations.
• Figure 3: Real-space matter kurto spectrum $\mathcal{P}_{3\times1}$ at $z=1$ from Quijote snapshots for $R_G=5 \ {\rm Mpc}/h$ (figure \ref{['fig:matter_3x1_RG5']}) and $R_G=10\ {\rm Mpc}/h$ (figure \ref{['fig:matter_3x1_RG10']}). All spectra are multiplied by $k^{2}$ for visual clarity. Top row: single realization. Bottom row: average over 40 realizations. Left panels: Quijote ODD_p (blue dots) and matched fiducial simulation (orange solid). Right panels: the difference of kurto spectra on ODD_p and fiducial simulations (blue dots).
• Figure 4: Redshift-space matter kurto spectrum $\mathcal{P}_{2\times 2}$ at $z=1$ from Quijote snapshots for $R=5 \ {\rm Mpc}/h$ (figure \ref{['fig:matter_RSD_2x2_RG5']}) and $R=10 \ {\rm Mpc}/h$ (figure \ref{['fig:matter_RSD_2x2_RG10']}). All spectra are multiplied by $k^2$ for visual clarity. Top row: single realization. Bottom row: average over 40 realizations. Left panels: Quijote ODD_p (blue dots) and matched fiducial simulation (orange solid). Right panels: the difference of kurto spectra on ODD_p and fiducial simulations (blue dots), with the gray lines being the measured real-space difference.
• Figure 6: Real-space halo kurto spectrum $\mathcal{P}_{2\times2}$ at $z=1$ from Quijote simulations for Gaussian smoothing scales $R_G=5\ {\rm Mpc}/h$ (figure \ref{['fig:halo_2x2_RG5']}) and $R_G=10 \ {\rm Mpc}/h$ (figure \ref{['fig:halo_2x2_RG10']}). All spectra are multiplied by $k^{2}$ for visual clarity. Top row: single realization. Bottom row: average over 500 realizations. Left panels: Quijote ODD_p (blue dots) and matched fiducial simulation (orange solid). Right panels: the total parity-odd signal from the fiducial-subtracted simulations (blue dots). The gray lines are the measured kurto spectra of the fiducial-subtracted matter field, scaled by a factor of $b_1^4$.