The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample

TL;DR

The paper delivers final, consensus cosmological constraints from the SDSS-III BOSS DR12 galaxy clustering data by unifying BAO (post-reconstruction) and full-shape (pre-reconstruction) analyses across three redshift slices. Leveraging 1.2 million galaxies over 9329 deg^2 and extensive mock catalogs, it achieves precise measurements of D_M/r_d, H r_d, and fσ8(z), tightly constraining curvature, dark energy, and growth. The results strongly favor a spatially flat ΛCDM universe with w ≈ -1, Ω_m ≈ 0.311, and H0 ≈ 67.6 km/s/Mpc, while placing a 95% CL upper limit on the sum of neutrino masses and testing GR-based growth via fσ8. By combining BAO, full-shape, Planck CMB, and SN data, the work demonstrates the power and self-consistency of large-scale structure as a cosmological probe and provides a robust framework for future surveys like DESI.

Abstract

We present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg^2 and volume of 18.7 Gpc^3, divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51, and 0.61. We measure the angular diameter distance DM and Hubble parameter H from the baryon acoustic oscillation (BAO) method after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the pre-reconstruction density field, we measure the product DM*H from the Alcock-Paczynski (AP) effect and the growth of structure, quantified by fσ8(z), from redshift-space distortions (RSD). We combine measurements presented in seven companion papers into a set of consensus values and likelihoods, obtaining constraints that are tighter and more robust than those from any one method. Combined with Planck 2015 cosmic microwave background measurements, our distance scale measurements simultaneously imply curvature Ω_K =0.0003+/-0.0026 and a dark energy equation of state parameter w = -1.01+/-0.06, in strong affirmation of the spatially flat cold dark matter model with a cosmological constant (ΛCDM). Our RSD measurements of fσ_8, at 6 per cent precision, are similarly consistent with this model. When combined with supernova Ia data, we find H0 = 67.3+/-1.0 km/s/Mpc even for our most general dark energy model, in tension with some direct measurements. Adding extra relativistic species as a degree of freedom loosens the constraint only slightly, to H0 = 67.8+/-1.2 km/s/Mpc. Assuming flat ΛCDM we find Ω_m = 0.310+/-0.005 and H0 = 67.6+/-0.5 km/s/Mpc, and we find a 95% upper limit of 0.16 eV/c^2 on the neutrino mass sum.

Figures (21)

• Figure 1: The footprint of the subsamples corresponding to the Northern and Southern galactic caps of the BOSS DR12 combined sample. The circles indicate the different pointings of the telescope and their colour corresponds to the sector completeness. The total area in the combined sample footprint, weighted by completeness, is 10,087 deg$^2$. Of these, 759 deg$^2$ are excluded by a series of veto masks, leaving a total effective area of 9329 deg$^2$. See ReidEtAl15 for further details on completeness calculation and veto masks.
• Figure 2: Number density of all four target classes assuming our fiducial cosmology with $\Omega_m = 0.31$, along with the sum of the CMASS and LOWZ number densities (black).
• Figure 3: BAO signals in the measured post-reconstruction power spectrum (left panels) and correlation function (right panels) and predictions of the best-fit BAO models (curves). To isolate the BAO in the monopole (top panels), predictions of a smooth model with the best-fit cosmological parameters but no BAO feature have been subtracted, and the same smooth model has been divided out in the power spectrum panel. For clarity, vertical offsets of $\pm 0.15$ (power spectrum) and $\pm 0.004$ (correlation function) have been added to the points and curves for the high- and low-redshift bins, while the intermediate redshift bin is unshifted. For the quadrupole (middle panels), we subtract the quadrupole of the smooth model power spectrum, and for the correlation function we subtract the quadrupole of a model that has the same parameters as the best-fit but with $\epsilon=0$. If reconstruction were perfect and the fiducial model were exactly correct, the curves and points in these panels would be flat; oscillations in the model curves indicate best-fit $\epsilon \neq 0$. The bottom panels show the measurements for the $0.4 < z < 0.6$ redshift bin decomposed into the component of the separations transverse to and along the line of sight, based on $x(p,\mu) = x_0(p)+L_2(\mu)x_2(p)$, where $x$ represents either $s^2$ multiplied by the correlation function or the BAO component power spectrum displayed in the upper panels, $p$ represents either the separation or the Fourier mode, $L_2$ is the 2nd order Legendre polynomial, $p_{||} = \mu p$, and $p_{\perp} = \sqrt{p^2-\mu^2p^2}$.
• Figure 4: Two-dimensional 68 and 95 per cent marginalized constraints on $D_M(z)\times(r_{d,{\rm fid}}/r_{d})$ and $H(z)\times (r_{d}/r_{d,{\rm fid}})$ obtained by fitting the BAO signal in the post-reconstruction monopole and quadrupole in configuration and Fourier space. The black solid lines represent the combination of these results into a set of consensus BAO-only constraints, as described in Section \ref{['sec:consensus_results']}. The blue solid lines correspond to the constraints inferred from the Planck CMB temperature and polarization measurements under the assumption of a $\Lambda$CDM model.
• Figure 5: The measured pre-reconstruction correlation function (left) and power spectrum (middle) in the directions perpendicular and parallel to the line of sight, shown for the NGC only in the redshift range $0.50<z<0.75$. In each panel, the color scale shows the data and the contours show the prediction of the best-fit model. The anisotropy of the contours seen in both plots reflects a combination of RSD and the AP effect, and holds most of the information used to separately constrain $D_M(z)/r_{d}$, $H(z)r_{d}$, and $f\sigma_8$. The BAO ring can be seen in two dimensions on the correlation function plot. To more clearly show the anisotropic BAO ring in the power spectrum, the right panel plots the two-dimensional power-spectrum divided by the best-fit smooth component. The wiggles seen in this panel are analogous to the oscillations seen in the top left panel of Fig \ref{['fig:pkxirecBAOfit']}.