Cosmology with the Galaxy Bispectrum Multipoles: Optimal Estimation and Application to BOSS Data

Abstract

We present a framework for self-consistent cosmological analyses of the full-shape anisotropic bispectrum, including the quadrupole ( = 2) and hexadecapole ( = 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 ΛCDM model, with a BBN prior on the baryon density and a Planck prior on n s , we can extract the remaining cosmological parameters directly from the clustering data. The inclusion of the unwindowed higher-order ( > 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 ≈ 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 ± 0.8 km s −1 Mpc −1 , Ω m = 0.33 ± 0.01 and σ 8 = 0.736 ± 0.033 (the tightest yet found in perturbative full-shape analyses). Our estimate of the growth parameter S 8 = 0.77 ± 0.04 agrees with both weak lensing and CMB results. The estimators and data used in this work have been made publicly available.

GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales

“…The single CW simulations with matter densities Ω m = {0.2, 0.27, 0.4, 1.0} feature the same initial conditions 18 . As further discussed in Appendix B, the CW simulations are only sufficiently accurate to study relative effects (variations with respect to the fiducial, Ω m = 0.27 simulation) and only up to k max = 0.11.…”

“…Hence, higher-order correlations, with the bispectrum as the most straightforward one, can yield further information about the evolution of structure in the universe. Specifically, the bispectrum of large-scale structure surveys can lift degeneracies between cosmological parameters, thus improving the precision in their inference [1][2][3][4][5][6][7][8][9][10][11][12][13][14], especially if the quadrupoles are added [15][16][17][18][19]. Moreover, it is the lowest order correlator which encloses primordial non-Gaussianity information [20][21][22].…”

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

“…D 'Amico et al (2022b) performed the first joint analysis of the monopole and quadrupole components of the power and bispectra measured from the BOSS DR12 galaxy data. More recently, Ivanov et al (2023) presented the results of an anisotropic bispectrum analysis including quadrupole and hexadecapole components measured from the BOSS DR12 data.…”

On approximations of the redshift-space bispectrum and power spectrum multipoles covariance matrix

“…A different "flavour" of diagonal covariance matrix is the so-called Gaussian covariance matrix which is not only diagonal but also non-linearities are neglected. Several studies have been using a Gaussian covariance matrix: either modelling it perturbatively [20,21] or using a Gaussian random field template (e.g., [22][23][24] for the 3-point correlation function, and [25] for the 2-point correlation function). In these (non-exhaustive) references, the choice of Gaussian covariance is justified by invoking the linearity of the scales present in the analysis.…”