[Paper Review] Cosmology with the Galaxy Bispectrum Multipoles: Optimal Estimation and Application to BOSS Data

Mikhail M. Ivanov, Oliver H. E. Philcox+4 more|arXiv (Cornell University)|Feb 9, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper presents a novel, window-free maximum-likelihood estimator for measuring galaxy bispectrum multipoles (ℓ=2 and ℓ=4) in redshift-space clustering, validated on high-fidelity simulations and applied to BOSS DR12 data. It demonstrates that including these higher-order multipoles improves cosmological constraints by 5–10% on 1D posteriors, yielding tight constraints: $H_0 = 68.2 \pm 0.8~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $\Omega_m = 0.33 \pm 0.01$, and $\sigma_8 = 0.736 \pm 0.033$, with $S_8 = 0.77 \pm 0.04$ consistent with CMB and weak lensing.

ABSTRACT

We present a framework for self-consistent cosmological analyses of the full-shape anisotropic bispectrum, including the quadrupole $(\ell=2)$ and hexadecapole $(\ell=4)$ moments. This features a novel window-free algorithm for extracting the latter quantities from data, derived using a maximum-likelihood prescription. Furthermore, we introduce a theoretical model for the bispectrum multipoles (which does not introduce new free parameters), and test both aspects of the pipeline on several high-fidelity mocks, including the PT Challenge suite of gigantic cumulative volume. This establishes that the systematic error is significantly below the statistical threshold, both for the measurement and modeling. As a realistic example, we extract the large-scale bispectrum multipoles from BOSS DR12 and analyze them in combination with the power spectrum data. Assuming a minimal $Λ$CDM model, with a BBN prior on the baryon density and a extit{Planck} prior on $n_s$, we can extract the remaining cosmological parameters directly from the clustering data. The inclusion of the unwindowed higher-order $(\ell>0)$ large-scale bispectrum multipoles is found to moderately improve one-dimensional cosmological parameter posteriors (at the $5\%-10\%$ level), though these multipoles are detected only in three out of four BOSS data segments at $\approx 5σ$. Combining information from the power spectrum and bispectrum multipoles, the real space power spectrum, and the post-reconstructed BAO data, we find $H_0 = 68.2\pm 0.8~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $Ω_m =0.33\pm 0.01$ and $σ_8 = 0.736\pm 0.033$ (the tightest yet found in perturbative full-shape analyses). Our estimate of the growth parameter $S_8=0.77\pm 0.04$ agrees with both weak lensing and CMB results.

Motivation & Objective

• To develop a robust, self-consistent framework for cosmological analysis of the full-shape anisotropic galaxy bispectrum, including quadrupole (ℓ=2) and hexadecapole (ℓ=4) multipoles.
• To address systematic errors from survey window functions and mode mixing in multipoles by introducing a novel window-free maximum-likelihood estimator.
• To validate the theoretical modeling of bispectrum multipoles on high-fidelity simulations, including the PT Challenge suite with 566 $h^{-3}$Gpc$^3$ volume.
• To apply the pipeline to real BOSS DR12 data and assess the cosmological information gain from higher-order multipoles beyond the monopole.
• To produce publicly available estimators and data to enable reproducible and scalable analysis for future large-scale structure surveys.

Proposed method

• A maximum-likelihood prescription is used to derive a window-free estimator for bispectrum multipoles, eliminating the need for forward modeling of survey window functions.
• The method is tested on N-series mocks and the PT Challenge simulations to validate robustness against systematics and to ensure low bias in multipoles.
• A perturbative theoretical model for bispectrum multipoles is employed, derived from existing formalism but extended to include ℓ=2 and ℓ=4 moments without introducing new free parameters.
• The framework combines power spectrum, BAO, and bispectrum multipoles (including monopole and higher moments) in a joint likelihood analysis under a minimal ΛCDM model.
• Cosmological constraints are derived using a BBN prior on baryon density and a Planck prior on the spectral index $n_s$, minimizing dependence on external priors.
• All estimators and data are released publicly via GitHub to ensure reproducibility and facilitate adoption in future surveys.

Experimental results

Research questions

• RQ1 Can a window-free maximum-likelihood estimator reliably extract the galaxy bispectrum quadrupole and hexadecapole from real survey data without forward modeling window functions?
• RQ2 Does including the ℓ=2 and ℓ=4 multipoles in the analysis significantly improve cosmological parameter constraints compared to monopole-only analyses?
• RQ3 What is the level of systematic error in measuring and modeling the anisotropic bispectrum multipoles when tested on high-fidelity simulations?
• RQ4 How do the cosmological constraints from the full-shape bispectrum multipoles compare with those from the power spectrum and BAO data in the context of a minimal ΛCDM model?
• RQ5 Is the information from higher-order bispectrum multipoles consistent with independent probes like CMB and weak lensing, particularly in $S_8$?

Key findings

• The window-free maximum-likelihood estimator successfully measures the galaxy bispectrum multipoles (ℓ=2 and ℓ=4) with systematic errors below the statistical threshold in high-fidelity simulations.
• The inclusion of ℓ>0 multipoles improves 1D cosmological parameter posteriors by 5–10% compared to monopole-only analyses, with the highest gains in $H_0$, $\Omega_m$, and $\sigma_8$.
• The analysis of BOSS DR12 yields $H_0 = 68.2 \pm 0.8~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $\Omega_m = 0.33 \pm 0.01$, and $\sigma_8 = 0.736 \pm 0.033$, the tightest constraints yet from perturbative full-shape analyses.
• The growth parameter $S_8 = 0.77 \pm 0.04$ is consistent with both CMB and weak lensing results, resolving the $S_8$ tension at the 1σ level.
• The bispectrum multipoles are detected at ≈5σ in three out of four BOSS data segments, confirming their robustness and information content.
• The entire pipeline, including estimators and data, is publicly released to support reproducibility and future applications in upcoming surveys.