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Could sample variance be responsible for the parity-violating signal seen in the Baryon Oscillation Spectroscopic Survey?

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Philosophical Transactions A
Authors:
Oliver Philcox at Columbia University
Oliver Philcox
J. Ereza
J. Ereza
J. Ereza
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Abstract

Recent works have uncovered an excess signal in the parity-odd four-point correlation function measured from the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy catalogue. If physical in origin, this could indicate new parity-breaking processes in inflation. At heart, these studies compare the observed four-point correlator with the distribution obtained from parity-conserving mock galaxy surveys; if the simulations underestimate the covariance of the data, noise fluctuations may be misinterpreted as a signal. To test this, we reanalyse the BOSS CMASS parity-odd dataset with the noise distribution model using the newly developed GLAM-Uchuu suite of mocks. These comprise full N-body simulations that follow the evolution of 20003 dark matter particles and represent a significant upgrade compared with the formerly used MultiDark-Patchy mocks, which were based on an alternative (non N-body) gravity solver. We find no significant evidence for parity-violation (with a baseline detection significance of 1.0σ), suggesting that the former signal (2.9σ with our data cuts) could be caused by an underestimation of the covariance in MultiDark-Patchy. The significant differences between results obtained with the two sets of BOSS-calibrated galaxy catalogues (whose covariances differ at the 10−20% level) showcase the heightened sensitivity of beyond-two-point analyses to nonlinear effects and indicate that previous constraints may suffer from large systematic uncertainties. This article is part of the discussion meeting issue ‘Challenging the standard cosmological model’.
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Could sample variance
be responsible for the
parity-violating signal seen
in the Baryon Oscillation
Spectroscopic Survey?
O. H. E. Philcox1,2,3 and J. Ereza4
1Department of Physics, Columbia University, New York, NY 10027, USA
2Simons Society of Fellows, Simons Foundation, New York, NY 10010, USA
3Department of Physics, Stanford University, Stanford, California 94305, USA
4Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, Granada
E-18080, Spain
OHEP,0000-0002-3033-9932
Recent works have uncovered an excess signal
in the parity-odd four-point correlation function
measured from the Baryon Oscillation Spectroscopic
Survey (BOSS) galaxy catalogue. If physical in
origin, this could indicate new parity-breaking
processes in inflation. At heart, these studies
compare the observed four-point correlator with the
distribution obtained from parity-conserving mock
galaxy surveys; if the simulations underestimate
the covariance of the data, noise fluctuations may
be misinterpreted as a signal. To test this, we
reanalyse the BOSS CMASS parity-odd dataset
with the noise distribution model using the newly
developed GLAM-Uchuu suite of mocks. These
comprise full -body simulations that follow the
evolution of 20003 dark matter particles and represent
a significant upgrade compared with the formerly
used MultiDark-Patchy mocks, which were based
on an alternative (non -body) gravity solver. We
find no significant evidence for parity-violation
(with a baseline detection significance of 1.0),
suggesting that the former signal (2.9 with our
data cuts) could be caused by an underestimation of
the covariance in MultiDark-Patchy. The significant
differences between results obtained with the two
sets of BOSS-calibrated galaxy catalogues (whose
covariances differ at the 10 −20% level) showcase
© 2025 The Author(s). Published by the Royal Society. All rights reserved.
royalsocietypublishing.org/journal/rsta
Research
Cite this article: Philcox OHE, Ereza J. 2025
Could sample variance be responsible for the
parity-violating signal seen in the Baryon
Oscillation Spectroscopic Survey? Phil. Trans. R.
Soc. A 383: 20240034.
https://doi.org/10.1098/rsta.2024.0034
Received: 31 May 2024
Accepted: 17 October 2024
One contribution of 12 to a discussion meeting
issue ‘Challenging the standard cosmological
model’.
Subject Areas:
cosmology
Keywords:
large-scale structure, correlation functions,
inflation, simulations
Author for correspondence:
O. H. E. Philcox
e-mail: ohep2@cantab.ac.uk
... Constructing these mocks accurately is challenging, given the as-sociated computational difficulty of producing accurate N-body simulations, and the modelling difficulty of populating these simulations with galaxies in a way that is accurate and takes into account systematic effects that enter during observation. More recently, [8] showed that the detection vanishes with the Uchuu-GLAM mocks [9], as opposed to the MultiDark-Patchy Mocks [10,11] used in previous studies. This highlights the sensitivity of the 4PCF approach to the choice of mock catalogs, which poses a significant challenge for the detection of parity violation. ...
... Equation 8 can also be viewed as the square root of the χ 2 for the case when the model expectation is zero, the data vector has been compressed into a scalar value, and the variance is measured not from external mocks. From this perspective, the model learns to estimate an analogue of the χ 2 directly from the data, similarly to the χ 2 -based approach for detecting parity violation used in previous work [5][6][7][8], but without the direct specification of the 4PCF. ...
... Equation 8 can also be viewed as the square root of the χ 2 for the case when the model expectation is zero, the data vector has been compressed into a scalar value, and the variance is measured not from external mocks. From this perspective, the model learns to estimate an analogue of the χ 2 directly from the data, similarly to the χ 2 -based approach for detecting parity violation used in previous work [5][6][7][8], but without the direct specification of the 4PCF. ...
Unsupervised Searches for Cosmological Parity Violation: Improving Detection Power with the Neural Field Scattering Transform
Preprint
Full-text available
  • May 2024
Recent studies using four-point correlations suggest a parity violation in the galaxy distribution, though the significance of these detections is sensitive to the choice of simulation used to model the noise properties of the galaxy distribution. In a recent paper, we introduce an unsupervised learning approach which offers an alternative method that avoids the dependence on mock catalogs, by learning parity violation directly from observational data. However, the Convolutional Neural Network (CNN) model utilized by our previous unsupervised approach struggles to extend to more realistic scenarios where data is limited. We propose a novel method, the Neural Field Scattering Transform (NFST), which enhances the Wavelet Scattering Transform (WST) technique by adding trainable filters, parameterized as a neural field. We first tune the NFST model to detect parity violation in a simplified dataset, then compare its performance against WST and CNN benchmarks across varied training set sizes. We find the NFST can detect parity violation with 4×4\times less data than the CNN and 32×32\times less than the WST. Furthermore, in cases with limited data the NFST can detect parity violation with up to 6σ6\sigma confidence, where the WST and CNN fail to make any detection. We identify that the added flexibility of the NFST, and particularly the ability to learn asymmetric filters, as well as the specific symmetries built into the NFST architecture, contribute to its improved performance over the benchmark models. We further demonstrate that the NFST is readily interpretable, which is valuable for physical applications such as the detection of parity violation.
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... [20] investigated whether lensing by a chiral gravitational-wave background could produce a signal. By analyzing the Uchuu mock catalogues, [21] proposed that the BOSS signal arises from sample variance rather than a physical origin. However, this analysis likely overestimated the covariance due to known limitations in mocks generated by replicating a smaller underlying box. ...
... 3 Appendix B of [22] demonstrates that even after rescaling the volume, the covariance of the 2-Point Correlation Function (2PCF) is overestimated by 10-15%. By scaling arguments, this would imply an even larger overestimation of the 4PCF covariance, order order of 20-30%, as claimed in [21]. ...
CMB Lensing Trispectrum as a Probe of Parity Violation in LSS
Preprint
  • May 2025
We show that the Cosmic Microwave Background (CMB) lensing trispectrum is sensitive to parity violation in Large-Scale Structure (LSS). We obtain a compact expression for the reduced lensing trispectrum that is general for any input matter trispectrum. We then present as an example a simple parity-violating toy model for the latter, and explicitly compute the parity-odd lensing trispectrum, including an estimate of the Signal-to-Noise Ratio (SNR). This work serves as a proof of principle, demonstrating how future studies of more physically motivated models can be conducted. It also provides an intuitive physical explanation of why CMB lensing is sensitive to parity. Our work is the first to point out that secondary CMB anisotropies can be used to probe parity in LSS, and will be important in enabling upcoming experiments such as Simons Observatory and CMB-S4 to contribute maximal power on parity violation.
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... Recently, two groups [11,12] have reported hints of parity violation in the galaxy 4PCF within the final data release of the BOSS galaxy survey [13], respectively, with statistical significance as high as 7.1σ and 2.9σ. On the other hand, a later analysis using an alternative set of mock catalogs found no support for parity violation [14]. Other follow-up studies, such as [15], come to the same conclusion. ...
Breaking Parity: the case of the Trispectrum from Chiral Scalar-Tensor Theories of Gravity
Preprint
  • Oct 2024
Recently, possible hints of parity violation have been observed in the connected galaxy four-point correlation function. Although the true origin of the signal from the analysis has been debated, should they have a physical origin, they might point to primordial non-Gaussianity and would be evidence of new physics. In this work, we examine the single-field slow-roll model of inflation within chiral scalar-tensor theories of modified gravity. These theories extend the Chern-Simons one by including parity-violating operators containing first and second derivatives of the non-minimally coupled scalar (inflaton) field. This model is capable of imprinting parity-violating signatures in late-time observables, such as the galaxy four-point correlation function. We perform an analysis of the graviton-mediated scalar trispectrum of the gauge-invariant curvature perturbation ζ(t,x)\zeta(t,\mathbf{x}). We estimate that for a set of parameters of the theory it is possible to produce a signal-to-noise ratio for the parity-violating part of the trispectrum of order one without introducing modifications to the single-field slow-roll setup. Even if the signal found in the analysis turns out to be spurious or if no parity violation is ever detected in the galaxy four-point correlation function, our analysis can be used to constrain the free parameters of these theories.
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... To compute E, we run the public ENCORE software [35] adapting the shell script available in the GitHub repository. 12 The strategy is to reduce the runtime by splitting the randoms into 32 equal files (after first randomizing their order to ensure that each random subset covers the full area). Then we compute counts of data powers D N (with N = 4 for the four-point function), random powers R N for the first random subset (for later use in edge correction), and data minus random powers (D − R) N for all 32 subsets. ...
No evidence for parity violation in BOSS
Preprint
Full-text available
  • Jul 2024
Recent studies have found evidence for parity violation in the BOSS spectroscopic galaxy survey, with statistical significance as high as 7σ7\sigma. These analyses assess the significance of the parity-odd four-point correlation function (4PCF) with a statistic called χ2\chi^2. This statistic is biased if the parity-even eight-point correlation function (8PCF) of the data differs from the mock catalogs. We construct new statistics χ×2\chi^2_\times, χnull2\chi^2_{\mathrm{null}} that separate the parity violation signal from the 8PCF bias term, allowing them to be jointly constrained. Applying these statistics to BOSS, we find that the parity violation signal ranges from 0 to 2.5σ2.5\sigma depending on analysis choices, whereas the 8PCF bias term is ∼6σ\sim 6\sigma. We conclude that there is no compelling evidence for parity violation in BOSS. Our new statistics can be used to search for parity violation in future surveys, such as DESI, without 8PCF biases.
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Doppler bias: impact of peculiar velocities on color selection and the large scale structure of galaxy surveys
Article
Lightcone selection effects on cosmic observables must be precisely accounted for in the next generation of surveys, including the Dark Energy Spectroscopic Instrument (DESI) survey. This will allow us to correctly model the data and extract subtle shifts from general-relativistic effects. We examine the effects of peculiar velocities on color selection in spectroscopic galaxy surveys, with a focus on their implications for the galaxy clustering dipole P 1 ( k ). Using DESI Emission Line Galaxy (ELG) targets, we show that peculiar velocities can shift spectral emission features into or out of filter bands, modifying galaxy colors and thereby changing galaxy selection. This phenomenon mimics the effect of evolution bias, and we refer to it as the Doppler bias, b D . The Doppler bias is of comparable size to the evolution bias at 0.8 < z < 1, where it is largest. This enhances the ELG-LRG (Luminous Red Galaxy) cross-correlation dipole by 25–50%. This could be detectable at the ∼ 6 σ level for the full DESI survey. Additionally, we found that our b D estimate is impacted by the incompleteness of the parent ELG sample. Therefore, this work highlights the essential need for careful consideration of spectral-dependent biases caused by peculiar velocities during the selection phase of galaxy surveys, to enable unbiased analyses.
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No evidence for parity violation in BOSS
Article
Full-text available
Recent studies have found evidence for parity violation in the BOSS spectroscopic galaxy survey, with statistical significance as high as 7σ. These analyses assess the significance of the parity-odd four-point correlation function (4PCF) with a statistic called X ². This statistic is biased if the parity-even eight-point correlation function (8PCF) of the data differs from the mock catalogs. We construct new statistics X ² ×, X ² null that separate the parity violation signal from the 8PCF bias term, allowing them to be jointly constrained. Applying these statistics to BOSS, we find that the parity violation signal ranges from 0 to 2.5σ depending on analysis choices, whereas the 8PCF bias term is ~ 6σ. We conclude that there is no compelling evidence for parity violation in BOSS. Our new statistics can be used to search for parity violation in future surveys, such as DESI, without 8PCF biases.
View
Parity-odd and even trispectrum from axion inflation
Article
Full-text available
The four-point correlation function of primordial scalar perturbations has parity-even and parity-odd contributions and the parity-odd signal in cosmological observations is opening a novel window to look for new physics in the inflationary epoch. We study the distinct parity-odd and even prediction from the axion inflation model, in which the inflaton couples to a vector field via a Chern-Simons interaction, and the vector field is considered to be either approximately massless (mA ≪ Hubble scale H) or very massive (mA ∼ H). The parity-odd signal arises due to one transverse mode of the vector field being predominantly produced during inflation. We adopt the in-in formalism to evaluate the correlation functions. Considering the vector field mode function to be dominated by its real part up to a constant phase, we simplify the formulas for numerical computations. The numerical studies show that the massive and massless vector fields give significant parity-even signals, while the parity-odd contribution is about one to two orders of magnitude smaller.
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Parity-violating trispectrum from Chern-Simons gravity
Article
Full-text available
A potential source for parity violation in the Universe is inflation. The simplest inflationary models have two fields: the inflaton and graviton, and the lowest-order parity-violating coupling between them is dynamical Chern-Simons (dCS) gravity with a decay constant f. Here, we show that dCS imprints a parity-violating signal in primordial scalar perturbations. Specifically, we find that, after dCS amplifies one graviton helicity due to a tachyonic instability, the graviton-mediated correlation between two pairs of scalars develops a parity-odd component. This correlation, the primordial scalar trispectrum, is then transferred to the corresponding curvature correlator and thus is imprinted in both large-scale structure (LSS) and the cosmic microwave background (CMB). We find that the parity-odd piece has roughly the same amplitude as its parity-even counterpart, scaled linearly by the degree of gravitational circular polarization Πcirc ∼ √ε[h ²/(M Pl f)] ≤ 1, with ε the slow-roll parameter, H the inflationary Hubble scale, and the upper bound saturated for purely circularly-polarized gravitons. We also find that, in the collapsed limit, the ratio of the two trispectra contains direct information about the graviton's spin. In models beyond standard inflationary dCS, e.g. those with multiple scalar fields or superluminal scalar sound speed, there can be a large enhancement factor F ≳ 10⁶ to the trispectrum. We find that an LSS survey that contains N modes linear modes would place an nσ constraint on Πcirc r of ∼ 0.04 (n/3)(10⁶/F)(10⁶/N modes)1/2 from the parity-odd galaxy trispectrum, for tensor-to-scalar ratio r. We also forecast for several spectroscopic and 21-cm surveys. This constraint implies that, for high-scale single-field inflation parameters, LSS can probe very large dCS decay constants f ≲ 4 × 10⁹ GeV(3/n)(F/10⁶)(N modes/10⁶)1/2. Our result is the first example of a massless particle yielding a parity-odd scalar trispectrum through spin-exchange.
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New shape of parity-violating graviton non-Gaussianity
Article
Full-text available
  • Oct 2023
  • J HIGH ENERGY PHYS
A bstract We show that the general vacuum states that respect the de Sitter symmetry, known as the α -vacua, can introduce non-vanishing parity-violating tensor non-Gaussianities. This is due to the mixing by the Bogoliubov transformation of the positive and negative frequency modes of the Bunch-Davies vacuum. We calculate explicitly the bispectra of tensor perturbations and show that the amplitude can be exponentially enhanced for certain choices of the squeezing parameter α and the phase ϕ of the α -vacua. We find a new shape for the parity-violating tensor bispectrum which peaks in the flattened configuration.
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The Uchuu - glam BOSS and eBOSS LRG lightcones: exploring clustering and covariance errors
Article
  • Jun 2024
  • MON NOT R ASTRON SOC
This study investigates the clustering and bias of Luminous Red Galaxies (LRG) in the BOSS-LOWZ, -CMASS, -COMB, and eBOSS samples, using two types of simulated lightcones: (i) high-fidelity lightcones from UchuuN-body simulation, employing SHAM technique to assign LRG to (sub)haloes, and (ii) 16 000 covariance lightcones from GLAM-UchuuN-body simulations, including LRG using HOD data from Uchuu. Our results indicate that Uchuu and glam lightcones closely replicate BOSS/eBOSS data, reproducing correlation function and power spectrum across scales from redshifts 0.2 to 1.0, from 2 to 150 h−1 Mpc150 \,h^{-1}\,\mathrm{Mpc} in configuration space, from 0.005 to 0.7 h Mpc−10.7\, h\,\mathrm{Mpc}^{-1} in Fourier space, and across different LRG stellar masses. Furthermore, comparing with existing MD-Patchy and EZmock BOSS/eBOSS lightcones based on approximate methods, our GLAM-Uchuu lightcones provide more precise clustering estimates. We identify significant deviations from observations within 20 h−1 Mpc20 \,h^{-1}\,\mathrm{Mpc} scales in MD-Patchy and EZmock, with our covariance matrices indicating that these methods underestimate errors by between 10 per cent and 60 per cent. Lastly, we explore the impact of cosmology on galaxy clustering. Our findings suggest that, given the current level of uncertainties in BOSS/eBOSS data, distinguishing models with and without massive neutrino effects on large-scale structure (LSS) is challenging. This paper highlights the Uchuu and GLAM-Uchuu simulations’ robustness in verifying the accuracy of Planck cosmological parameters, providing a strong foundation for enhancing lightcone construction in future LSS surveys. We also demonstrate that generating thousands of galaxy lightcones is feasible using N-body simulations with adequate mass and force resolution.
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Testing parity symmetry with the polarized cosmic microwave background
Article
  • Apr 2024
New physics in the early Universe could lead to parity-violation in the late Universe, sourcing statistics whose sign changes under point reflection. The best constraints on such phenomena have come from the Planck temperature fluctuations; however, this is already cosmic-variance limited down to relatively small scales. Thus only small improvements are expected in the future. Here, we search for signatures of parity violation in the polarized cosmic microwave background, using the Planck PR4 T- and E-mode data. We perform both a simulation-based blind test for any parity-violating signal at ℓ<518, and a targeted search for primordial U(1) gauge fields (and the amplitudes of a generic collapsed model) at ℓ<2000. In all cases, we find no evidence for new physics, with the model-independent test finding consistency with the FFP10/NPIPE simulation suite at (−)0.4σ, and the gauge field test constraining the fractional amplitude of gauge fields during inflation to be below 6×10−19 at 95% confidence level for a fiducial model. The addition of polarization data can significantly improve the constraints, depending on the particular model of primordial physics, and the bounds will tighten significantly with the inclusion of smaller-scale information.
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What can galaxy shapes tell us about physics beyond the standard model?
Article
  • Mar 2024
The shapes of galaxies trace scalar physics in the late-Universe through the large-scale gravitational potential. Are they also sensitive to higher-spin physics? We present a general study into the observational consequences of vector and tensor modes in the early and late Universe, through the statistics of cosmic shear and its higher-order generalization, flexion. Higher-spin contributions arise from both gravitational lensing and intrinsic alignments, and we give the leading-order correlators for each (some of which have been previously derived), in addition to their flat-sky limits. In particular, we find nontrivial sourcing of shear EB and BB spectra, depending on the parity properties of the source. We consider two sources of vector and tensor modes: scale-invariant primordial fluctuations and cosmic strings, forecasting the detectability of each for upcoming surveys. Shear is found to be a powerful probe of cosmic strings, primarily through the continual sourcing of vector modes; flexion adds little to the constraining power except on very small scales (ℓ≳1000), though it could be an intriguing probe of as-yet-unknown rank-three tensors or halo-scale physics. Such probes could be used to constrain new physics proposed to explain recent pulsar timing array observations.
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Testing graviton parity and Gaussianity with Planck T -, E -, and B -mode bispectra
Article
  • Mar 2024
Many inflationary theories predict a non-Gaussian spectrum of primordial tensor perturbations, sourced from nonstandard vacuum fluctuations, modified general relativity, or new particles such as gauge fields. Several such models also predict a chiral spectrum in which one polarization state dominates. In this work, we place constraints on the non-Gaussianity and parity properties of primordial gravitational waves utilizing the Planck PR4 temperature and polarization data set. Using recently developed quasioptimal bispectrum estimators, we compute binned parity-even and parity-odd bispectra for all combinations of cosmic microwave background (CMB) T-, E-, and B-modes with 2≤ℓ<500, and perform both blind tests, sensitive to arbitrary three-point functions, and targeted analyses of a well-motivated equilateral gravitational-wave template (sourced by gauge fields) with amplitude fNLttt. This is the first time B-modes have been included in primordial non-Gaussianity analyses; they are found to strengthen constraints on the parity-even sector by ≃30% and dominate the parity-odd bounds, without inducing bias. We report no detection of non-Gaussianity (of either parity), with the template amplitude constrained to fNLttt=900±700 (stable with respect to a number of analysis variations), compared to 1300±1200 in Planck 2018. The methods applied herein can be reapplied to upcoming CMB data sets such as LiteBIRD, with the inclusion of B-modes poised to dramatically improve future bounds on tensor non-Gaussianity.
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Signatures of a parity-violating universe
Article
  • Jan 2024
What would a parity-violating universe look like? We present a numerical and theoretical study of mirror asymmetries in the late universe, using a new suite of N-body simulations: quijote-odd. These feature parity-violating initial conditions, injected via a simple ansatz for the imaginary primordial trispectrum and evolved into the nonlinear regime. We find that the realization-averaged power spectrum, bispectrum, halo mass function, and matter PDF are not affected by our modifications to the initial conditions, deep into the nonlinear regime, which we argue arises from rotational and translational invariance. In contrast, the parity-odd trispectrum of matter (measured using a new estimator), shows distinct signatures proportional to the parity-violating parameter, pNL, which sets the amplitude of the primordial trispectrum; furthermore, the statistic cannot be sourced by any conventional gravitational or baryonic processes. We additionally find intriguing signatures in the angular momentum of halos, with the primordial trispectrum inducing a nonzero correlation between angular momentum and smoothed velocity field, proportional to pNL. Our simulation suite has been made public to facilitate future analyses.
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Do the CMB Temperature Fluctuations Conserve Parity?
Article
  • Nov 2023
Observations of the cosmic microwave background (CMB) have cemented the notion that the large-scale Universe is both statistically homogeneous and isotropic. But is it invariant also under reflections? To probe this we require parity-sensitive statistics: for scalar observables, the simplest is the trispectrum. We make the first measurements of the parity-odd scalar CMB, focusing on the large-scale (2<ℓ<510) temperature anisotropies measured by Planck. This is facilitated by new quasi-maximum-likelihood estimators for binned correlators, which account for mask convolution and leakage between even- and odd-parity components, and achieve ideal variances within ≈20%. We perform a blind test for parity violation by comparing a χ2 statistic from Planck to theoretical expectations, using two suites of simulations to account for the possible likelihood non-Gaussianity and residual foregrounds. We find consistency at the ≈0.4σ level, yielding no evidence for novel early-Universe phenomena. The measured trispectra allow for a wealth of new physics to be constrained; here, we use them to constrain eight primordial models, including ghost inflation, cosmological collider scenarios, and Chern-Simons gauge fields. We find no signatures of new physics, with a maximal detection significance of 2.0σ. Our results also indicate that the recent parity excesses seen in the BOSS galaxy survey are not primordial in origin, given that the CMB dataset contains roughly 250× more primordial modes, and is far easier to interpret, given the linear physics, Gaussian statistics, and accurate mocks. Tighter CMB constraints can be wrought by including smaller scales (though rotational invariance washes out the flat-sky limit) and adding polarization data.
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