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

We present a framework for self-consistent cosmological analyses of the full-shape anisotropic bispectrum, including the quadrupole $(\mathrm{\ell }=2)$ and hexadecapole $(\mathrm{\ell }=4)$ 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 $\mathrm{\Lambda }$CDM model, with a BBN prior on the baryon density and a $\mathit{\text{Planck}}$ prior on $n_s$, we can extract the remaining cosmological parameters directly from the clustering data. The inclusion of the unwindowed higher-order $(\mathrm{\ell }>0)$ large-scale bispectrum multipoles is found to moderately improve one-dimensional cosmological parameter posteriors (at the $5\mathrm{\%}-10\mathrm{\%}$ level), though these multipoles are detected only in three out of four BOSS data segments at $\approx 5\sigma$. Combining information from the power spectrum and bispectrum multipoles, the real space power spectrum, and the post-reconstructed BAO data, we find $H_0=68.2\pm 0.8\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$, ${\mathrm{\Omega }}_m=0.33\pm 0.01$ and ${\sigma }_8=0.736\pm 0.033$ (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.