The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large-scale two-point correlation function

TL;DR

Using the CMASS DR9 sample, the authors measure the monopole of the redshift-space two-point correlation function $\xi(s)$ and fit it with a Renormalized Perturbation Theory–based full-shape model to extract cosmological information. They combine this with external probes including CMB, SN, and BAO to test ΛCDM and extensions, finding no significant deviations from flat ΛCDM and achieving tight constraints such as $\Omega_k=-0.0043\pm0.0049$, $f_ν<0.049$ (95% CL), $r<0.16$ (95% CL), and $n_s=0.962\pm0.009$ in the base model. The dark energy sector remains consistent with a cosmological constant, with $w_{\rm DE}=-1.033\pm0.073$ when all data are combined and no evidence for time evolution $w_{\rm DE}(a)$ beyond small uncertainties. The results illustrate the power of current cosmological observations, especially the CMASS full-shape clustering, to break degeneracies and tightly constrain fundamental parameters while supporting the standard $\Lambda$CDM paradigm. The analysis also highlights small hemispheric differences in clustering, likely statistical, and points to future data releases and Planck-era measurements as avenues to further sharpen these constraints.

Abstract

We obtain constraints on cosmological parameters from the spherically averaged redshift-space correlation function of the CMASS Data Release 9 (DR9) sample of the Baryonic Oscillation Spectroscopic Survey (BOSS). We combine this information with additional data from recent CMB, SN and BAO measurements. Our results show no significant evidence of deviations from the standard flat-Lambda CDM model, whose basic parameters can be specified by Omega_m = 0.285 +- 0.009, 100 Omega_b = 4.59 +- 0.09, n_s = 0.96 +- 0.009, H_0 = 69.4 +- 0.8 km/s/Mpc and sigma_8 = 0.80 +- 0.02. The CMB+CMASS combination sets tight constraints on the curvature of the Universe, with Omega_k = -0.0043 +- 0.0049, and the tensor-to-scalar amplitude ratio, for which we find r < 0.16 at the 95 per cent confidence level (CL). These data show a clear signature of a deviation from scale-invariance also in the presence of tensor modes, with n_s <1 at the 99.7 per cent CL. We derive constraints on the fraction of massive neutrinos of f_nu < 0.049 (95 per cent CL), implying a limit of sum m_nu < 0.51 eV. We find no signature of a deviation from a cosmological constant from the combination of all datasets, with a constraint of w_DE = -1.033 +- 0.073 when this parameter is assumed time-independent, and no evidence of a departure from this value when it is allowed to evolve as w_DE(a) = w_0 + w_a (1 - a). The achieved accuracy on our cosmological constraints is a clear demonstration of the constraining power of current cosmological observations.

Figures (15)

• Figure 1: The sky coverage, in Galactic coordinates, of the CMASS DR9 spectroscopic sample used in this analysis in the northern (left panel) and southern (right panel) Galactic hemispheres. Different sectors are colour-coded according to their completeness. The low completeness at many edges is due to planned but currently unobserved tiles that will overlap the current geometry. The light grey shaded region shows the expected footprint of the final survey, totalling 10,269 deg$^2$.
• Figure 2: Panel (a): spherically averaged redshift-space two-point correlation function of the full CMASS sample. The errorbars were obtained from a set of 600 mock catalogues constructed to follow the same selection function of the survey Manera2012. The dashed line corresponds to the best-fitting $\Lambda$CDM model obtained by combining the information from the shape of the correlation function and CMB measurements (see Section \ref{['ssec:lcdm']}). Panel (b): same as panel (a), but rescaled by $(s/s_{\rm BAO})^2$, where $s_{\rm BAO}=153.2 \, {\rm Mpc}$ (which corresponds to 107.2 $h^{-1}{\rm Mpc}$), to highlight the baryonic acoustic feature.
• Figure 3: Panel (a): mean correlation function from our ensemble of mock catalogues obtained by assuming the true cosmological parameters as fiducial values (circles connected by a solid line) and a flat cosmology with $\Omega_{\rm m}=0.4$ (squares connected by a dashed line). The shaded region correspond to the variance between the different realizations of the ensemble. Panel (b): same measurements as panel (a), but expressed as a function of $y=s/D_{\rm V}(z_{\rm m})$, which removes the dependence on the fiducial cosmology.
• Figure 4: The 68 and 95 per cent marginalized constraints in the $\omega_{\rm m}-D_{\rm V}(z_{\rm m})$ plane, where $\omega_{\rm m}\equiv \Omega_{\rm m} h^2$, obtained from the shape of the CMASS correlation function alone (solid lines). The dashed, dot-dashed and dotted lines correspond to constant values of $D_{\rm v}(z_{\rm m})\,\omega_{\rm m}$, $y_{\rm s}(z_{\rm m})$ (equation \ref{['eq:ys']}), and $A(z_{\rm m})$ (equation \ref{['eq:apar']}), respectively.
• Figure 5: The marginalized constraints in the $\Omega_{\rm m}-h$ plane for the $\Lambda$CDM parameter set. The dashed lines show the 68 and 95 per cent contours obtained using CMB information alone. The solid contours correspond to the results obtained from the combination of CMB data plus the shape of the CMASS $\xi(s)$.