The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the Fourier space wedges of the final sample

TL;DR

This work presents a full-shape analysis of anisotropic clustering in Fourier space using the final BOSS DR12 galaxy sample. By extending clustering wedges to Fourier space with FFT-based estimators and a gRPT+RSD modelling framework, the authors measure distances and growth rates across three redshift bins while incorporating realistic survey windows and mock-based covariances. The results yield tight ΛCDM constraints and robust limits on extensions including dynamical dark energy, curvature, modified gravity, and neutrino properties, all consistent with Planck and SN data. The methodology enhances the exploitation of galaxy clustering data and lays groundwork for future, larger-volume surveys.

Abstract

We extract cosmological information from the anisotropic power spectrum measurements from the recently completed Baryon Oscillation Spectroscopic Survey (BOSS), extending the concept of clustering wedges to Fourier space. Making use of new FFT-based estimators, we measure the power spectrum clustering wedges of the BOSS sample by filtering out the information of Legendre multipoles l > 4. Our modelling of these measurements is based on novel approaches to describe non-linear evolution, bias, and redshift-space distortions, which we test using synthetic catalogues based on large-volume N-body simulations. We are able to include smaller scales than in previous analyses, resulting in tighter cosmological constraints. Using three overlapping redshift bins, we measure the angular diameter distance, the Hubble parameter, and the cosmic growth rate, and explore the cosmological implications of our full shape clustering measurements in combination with CMB and SN Ia data. Assuming a ΛCDM cosmology, we constrain the matter density to Ω_m = 0.311 -0.010 +0.009 and the Hubble parameter to H_0 = 67.6 -0.6 +0.7 km s^-1 Mpc^-1, at a confidence level (CL) of 68 per cent. We also allow for non-standard dark energy models and modifications of the growth rate, finding good agreement with the ΛCDM paradigm. For example, we constrain the equation-of-state parameter to w = -1.019 -0.039 +0.048. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. 2016 to produce the final cosmological constraints from BOSS.

Figures (21)

• Figure 1: The power spectrum wedges computed by filtering out the information of Legendre multipoles $\ell>4$ for NGC (upper panels) and SGC (lower panels) of the BOSS DR12 combined sample in the low (left-hand panels), intermediate (centre panels), and high (right-hand panels) redshift bins defined in Table \ref{['tab:dr12_z_ranges']}. The error bars are derived as the square root of the diagonal entries of MD-Patchy covariance matrix (see section \ref{['sec:covariance_matrix']}). The theoretical predictions are based on the model described in section \ref{['sec:model']} and for the maximum-likelihood BAO+RSD parameters using a best-fit Planck2015 input power spectrum. The low redshift bin fits use separate bias, RSD, and shot noise parameters for NGS and SGC, whereas the intermediate and high bins use only one set of nuisance parameters.
• Figure 2: MD-Patchy power spectrum wedges derived from the multipoles $P_{\ell=0,2,4}(k)$ compared against the results of the BOSS DR12 combined sample for the low (upper panel) and high (lower panel) redshift bin. These measurements correspond to 2045 full survey (combining NGC and SGC) mocks and have been performed assuming the fiducial cosmology.
• Figure 3: Correlation matrix of the MD-Patchy power spectrum wedges derived from the power spectrum multipoles $P_{\ell=0,2,4}(k)$ for the high redshift bin. As in Fig. \ref{['fig:patchy_ps_wedges']}, for this measurement NGC and SGC have been combined for simplicity. The correlation matrix for the low redshift bin looks similar.
• Figure 4: The window matrix $w_{3\mathrm{w},nm}(k_i,k')$ of the DR12 combined sample for the most-perpendicular wedge in the upper panel and for all wedges in the lower panel. The upper panel shows the dependency of $w_{3\mathrm{w},11}$ on the redshift range and the mean $k_i$ (given in $h \, \unit{Mpc}^{-1}$) of the output bin. The window matrices of each redshift bin are similar (dashed lines -- low redshift bin, solid lines -- high redshift bin). The lower panel shows the contributions of the different input wedges to the output wedges for the bin $k_i = 0.0275$ (from left to right, the $x$-axis is split into repeating intervals for better visibility). The SGC window matrix resembles that of the NGC, but the suppression of power is slightly stronger as the volume is smaller (see also Fig. \ref{['fig:pk_conv_dr12_comb']}).
• Figure 5: The effect of the window matrix $w_{3\mathrm{w},nm}$ for the DR12 combined sample on the Fourier space wedges in the high redshift bin. The solid lines are the theoretical predictions $\tilde{P}_{3\mathrm{w},n}(k')$ (using the model described in section \ref{['sec:zspace_clustering_model']} for best-fitting $\Lambda$CDM parameters), and the dashed (dash-dotted) lines corresponds to the prediction convolved with the window function, $\hat{P}_{3\mathrm{w},n}(k_i)$, for the Northern (Southern) galactic cap.