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 (<math display="inline"><mrow><mo>ℓ</mo><mo>=</mo><mn>2</mn></mrow></math>) and hexadecapole (<math display="inline"><mrow><mo>ℓ</mo><mo>=</mo><mn>4</mn></mrow></math>) 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 <math display="inline"><mi mathvariant="normal">Λ</mi><mi>CDM</mi></math> model, with a BBN prior on the baryon density and a Planck prior on <math display="inline"><msub><mi>n</mi><mi>s</mi></msub></math>, we can extract the remaining cosmological parameters directly from the clustering data. The inclusion of the unwindowed higher-order (<math display="inline"><mrow><mo>ℓ</mo><mo>&gt;</mo><mn>0</mn></mrow></math>) 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 <math display="inline"><mo>≈</mo><mn>5</mn><mi>σ</mi></math>. Combining information from the power spectrum and bispectrum multipoles, the real space power spectrum, and the postreconstructed BAO data, we find <math display="inline"><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>68.2</mn><mo>±</mo><mn>0.8</mn><mtext> </mtext><mtext> </mtext><mi>km</mi><mtext> </mtext><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mtext> </mtext><msup><mrow><mi>Mpc</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math>, <math display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>m</mi></msub><mo>=</mo><mn>0.33</mn><mo>±</mo><mn>0.01</mn></math> and <math display="inline"><msub><mi>σ</mi><mn>8</mn></msub><mo>=</mo><mn>0.736</mn><mo>±</mo><mn>0.033</mn></math> (the tightest yet found in perturbative full-shape analyses). Our estimate of the growth parameter <math display="inline"><msub><mi>S</mi><mn>8</mn></msub><mo>=</mo><mn>0.77</mn><mo>±</mo><mn>0.04</mn></math> agrees with both weak lensing and CMB results. The estimators and data used in this work have been made publicly available.