The BOSS DR12 Full-Shape Cosmology: $Λ$CDM Constraints from the Large-Scale Galaxy Power Spectrum and Bispectrum Monopole

TL;DR

This work delivers the most complete full-shape ΛCDM analysis of BOSS DR12 to date by jointly modeling the redshift-space power spectrum multipoles, a real-space power proxy, BAO information from reconstructed spectra, and the bispectrum monopole using window-free estimators. Leveraging the EFTofLSS framework, it achieves tight constraints on H_0 and σ_8 (with σ_8 reaching sub-5% precision when Planck n_s priors are included) and provides refined higher-order galaxy-bias parameters, all while showing consistency with Planck within uncertainties and with weak-lensing results for S_8. The study demonstrates the robustness of the methodology through extensive mock tests and discusses the implications for potential new physics, neutrino mass, and primordial non-Gaussianity, highlighting avenues for future DESI/Euclid analyses. Overall, the paper establishes a rigorous, window-free, full-shape pipeline that can probe beyond-ΛCDM physics while delivering reliable cosmological constraints from current galaxy surveys.

Abstract

We present a full $Λ$CDM analysis of the BOSS DR12 dataset, including information from the power spectrum multipoles, the real-space power spectrum, the reconstructed power spectrum and the bispectrum monopole. This is the first analysis to feature a complete treatment of the galaxy bispectrum, including a consistent theoretical model and without large-scale cuts. Unlike previous works, the statistics are measured using window-free estimators: this greatly reduces computational costs by removing the need to window-convolve the theory model. Our pipeline is tested using a suite of high-resolution mocks and shown to be robust and precise, with systematic errors far below the statistical thresholds. Inclusion of the bispectrum yields consistent parameter constraints and shrinks the $σ_8$ posterior by $13\%$ to reach $<5\%$ precision; less conservative analysis choices would reduce the error-bars further. Our constraints are broadly consistent with Planck: in particular, we find $H_0 = 69.6^{+1.1}_{-1.3}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $σ_8 = 0.692^{+0.035}_{-0.041}$ and $n_s=0.870^{+0.067}_{-0.064}$, including a BBN prior on the baryon density. When $n_s$ is set by Planck, we find $H_0 = 68.31^{+0.83}_{-0.86}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ and $σ_8 = 0.722^{+0.032}_{-0.036}$. Our $S_8$ posterior, $0.751\pm0.039$, is consistent with weak lensing studies, but lower than Planck. Constraints on the higher-order bias parameters are significantly strengthened from the inclusion of the bispectrum, and we find no evidence for deviation from the dark matter halo bias relations. These results represent the most complete full-shape analysis of BOSS DR12 to-date, and the corresponding spectra will enable a variety of beyond-$Λ$CDM analyses, probing phenomena such as the neutrino mass and primordial non-Gaussianity.

Figures (12)

• Figure 1: $\Lambda$CDM parameter constraints from the full BOSS DR12 galaxy dataset, using the following combinations of statistics, as well as a BBN prior on the baryon density: the (window-free) redshift-space power spectrum $P_\ell$ up to $k_{\rm max} = 0.2h\,\mathrm{Mpc}^{-1}$ (gray), the above plus the real-space power spectrum proxy $Q_0$ (green) up to $k_{\rm max} = 0.4h\,\mathrm{Mpc}^{-1}$ (green), the above plus BAO parameters from the post-reconstructed power spectrum (blue), the above plus the bispectrum monopole $B_0$ up to $k_{\rm max} = 0.08h\,\mathrm{Mpc}^{-1}$ (red). The bispectrum is the main new feature of this work, and leads to a tightening of $\sigma_8$ by $\approx 10\%$, with the modest improvement linked to our conservative analysis choices. The $\sigma_8$ posteriors are $\approx 1\sigma$ larger than those found in some former analyses; this is due to an error in the public power spectra, as discussed in §\ref{['subsec: comparison']}. Tab. \ref{['tab: main-results']} gives the associated marginalized posteriors for each analysis shown above.
• Figure 2: Measured power spectra (top) and bispectra (bottom) from the BOSS dataset (points) and 2048 Patchy mocks (lines and shaded regions) for two redshift bins 'z1' (left) and 'z3' (right). For the power spectra, we show measurements from the monopole, quadrupole, and hexadecapole, in red, blue, and green respectively, as well as the $Q_0$ statistic, $Q_0(k)\equiv P_0(k)-(1/2)P_2(k)+(3/8)P_4(k)$, which is a proxy for the real-space power spectrum. The vertical line disambiguates regions fit with the full power spectrum multipoles (left) and those with $Q_0$; the other regions (shown in faint lines) are not used in the analysis. For bispectra, we plot all triangle bins included in the analysis with $k<0.08h\,\mathrm{Mpc}^{-1}$, noting that the observed structure arises from the bin ordering. These are ordered by triangle side, with scalene, isosceles, and equilateral triangles shown in green, blue, and red respectively. The red numbers in the right panel give the value of $k$ for each equilateral bin. For clarity, we have combined estimates from the NGC and SGC regions (weighting by their sky fractions, with $f_{\rm NGC}\approx 0.7$); these are treated as separate samples in the main analysis of this work.
• Figure 3: Constraints on cosmological and bias parameters extracted from the power spectrum and bispectrum of 84 Nseries simulations, with a covariance matrix rescaled to match the total volume of BOSS (blue), and that of the Nseries suite (red). Dashed lines mark fiducial values of cosmological parameters, and we give the marginalized limits in Tab. \ref{['tab:nseries']}. Notably, any systematic effects are strongly subdominant for the BOSS-scaled posteriors, though there are slight shifts for the full Nseries volume (which is somewhat larger than the full DESI dataset).
• Figure 4: Correlation matrices for the power spectrum and bispectrum measurements used in this work, computed using 2048 Patchy simulations. The left (right) plot gives the result for the 'z1' ('z3') redshift slice, averaging together NGC and SGC measurements for visibility, as in Fig. \ref{['fig: pk-bk-plot']}. The correlation matrix is defined $R_{ij} \equiv C_{ij}/\sqrt{C_{ii}C_{jj}}$ for covariance $C_{ij}$. Here the first through third submatrices show the results from the power spectrum monopole, quadrupole and hexadecapole respectively, the fourth gives the result from the real-space power spectrum, $Q_0$, whilst the fifth gives that from the bispectrum. For clarity, we omit the BAO parameters, whose covariance with the windowed spectra can be found in 2020JCAP...05..032P. In each case, we include only $k$-modes used in the analysis below; i.e. we use $0.01\leq k\leq 0.20$ for $P_\ell$, $0.20\leq k\leq 0.4$ for $Q_0$ and $0.01\leq k\leq 0.08$ for $B_0$ (in $h\,\mathrm{Mpc}^{-1}$ units). In general, there is little off-diagonal correlation, except for the $Q_0$ statistic which involves smaller scale information. Note that the correlation is less than conventionally found, since our measurements are not window convolved; however, the 'z1' and 'z3' covariances appear somewhat different, due to both the different redshift, and selection functions of the two.
• Figure 5: Cosmological parameter constraints from the $\Lambda$CDM analysis of BOSS data, including the power spectrum ($P_\ell$), real-space power spectrum analog ($Q_0$), BAO parameters from reconstructed spectra (BAO), and the bispectrum monopole ($B_0$). The marginalized constraints are given in Tab. \ref{['tab: free-ns']}. As found previously, the addition of $Q_0$ gives a slight decrease in the posterior volume (limited mostly by shot-noise), whilst BAO parameters help to reduce the $H_0$ contour, and the bispectrum gives a $13\%$ reduction in the $\sigma_8$ error-bar. Notably, the spectral slope is poorly constrained and degenerate with other parameters; results with a Planck prior on $n_s$ are shown in Fig. \ref{['fig: boss-fix-ns']}.