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 quadrupole $(\ell=2)$ and hexadecapole $(\ell=4)$ moments. This features novel window-free algorithm extracting latter quantities from data, derived using maximum-likelihood prescription. Furthermore, we introduce theoretical model bispectrum multipoles (which does not new free parameters), test both aspects pipeline on several high-fidelity mocks, PT Challenge suite gigantic cumulative volume. establishes that systematic error is significantly below statistical threshold, measurement modeling. As realistic example, extract large-scale BOSS DR12 analyze them in combination with power spectrum data. Assuming minimal $\Lambda$CDM model, BBN prior baryon density \textit{Planck} $n_s$, can remaining parameters directly clustering The inclusion unwindowed higher-order $(\ell>0)$ found to moderately improve one-dimensional parameter posteriors (at $5\%-10\%$ level), though these are detected only three out four data segments at $\approx 5\sigma$. Combining information multipoles, real space spectrum, post-reconstructed BAO find $H_0 = 68.2\pm 0.8~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $\Omega_m =0.33\pm 0.01$ $\sigma_8 0.736\pm 0.033$ (the tightest yet perturbative analyses). Our estimate growth $S_8=0.77\pm 0.04$ agrees weak lensing CMB results.