The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: single-probe measurements and the strong power of normalized growth rate on constraining dark energy

TL;DR

This paper demonstrates that anisotropic galaxy clustering in the SDSS-III/BOSS DR9 CMASS sample yields model-independent constraints on the expansion history via $H(z)$ and $D_A(z)$, and on structure growth through $f(z)\sigma_8(z)$, using only CMASS data at an effective redshift $z=0.57$. The authors construct a full forward-model of the 2D correlation function, including non-linear BAO damping, redshift-space distortions, and Fingers-of-God, and they estimate the covariance from 600 mock catalogs. They report CMASS-only measurements and derive covariances, then show how to combine these single-probe results with CMB data to constrain dark energy models (ΛCDM, wCDM, etc.), highlighting that inclusion of $f(z)\sigma_8(z)$ significantly enhances dark energy constraints and helps break degeneracies. The work provides a practical framework, including CosmoMC code, for single-probe, model-independent analyses that can be applied to current and upcoming surveys, with results consistent with ΛCDM and valuable guidance for joint analyses with other probes.

Abstract

We present measurements of the anisotropic galaxy clustering from the Data Release 9 (DR9) CMASS sample of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). We analyze the broad-range shape of the monopole and quadrupole correlation functions to obtain constraints, at the effective redshift $z=0.57$ of the sample, on the Hubble expansion rate $H(z)$, the angular-diameter distance $D_A(z)$, the normalized growth rate $f(z)σ_8(z)$, the physical matter density $Ω_m h^2$, and the biased amplitude of matter fluctuation bσ_8(z). We obtain {$H(0.57)$, $D_A(0.57)$, $f(0.57)σ_8(0.57)$, $Ω_m h^2$, $bσ_8(0.57)$} = {$87.6_{-6.8}^{+6.7}$, $1396\pm73$, $0.126_{-0.010}^{+0.008}$, $1.19\pm0.14$, $0.428\pm0.066$} and their covariance matrix as well. The parameters which are not well constrained by our of galaxy clustering analysis are marginalized over with wide flat priors. Since no priors from other data sets (i.e., CMB) are adopted and no dark energy models are assumed, our results from BOSS CMASS galaxy clustering alone may be combined with other data sets, i.e. CMB, SNe, lensing or other galaxy clustering data to constrain the parameters of a given cosmological model. We show that the major power on constraining dark energy from the anisotropic galaxy clustering signal, as compared to the angular-averaged one (monopole), arises from including the normalized growth rate $f(z)σ_8(z)$. In the case of the wCDM cosmological model our single-probe CMASS constraints, combined with CMB (WMAP9+SPT), yield a value for the dark energy equation of state parameter of $w=-0.90\pm0.11$. Therefore, it is important to include $f(z)σ_8(z)$ while investigating the nature of dark energy with current and upcoming large-scale galaxy surveys.

Figures (5)

• Figure 1: Measurement of effective monopole (left) and quadrupole (right) of the correlation function for the BOSS DR9 CMASS galaxy sample (black points), compared to the the theoretical model given the parameters measured (solid line). The error bars are the square roots of the diagonal elements of the covariance matrix (see Sec. \ref{['sec:covar']}). In this study, our fitting scale range is $40h^{-1}$Mpc $<s<160h^{-1}$Mpc.
• Figure 2: 2D marginalized contours for $68\%$ and $95\%$ confidence levels for $\Omega_k$ and $\Omega_m$ (o$\Lambda$CDM model assumed) from WMAP9+SPT (red), CMASS (green), and WMAP9+SPT+CMASS (blue). The CMASS data break the degeneracy between $\Omega_k$ and $\Omega_m$ constrained by CMB data.
• Figure 3: 2D marginalized contours for $68\%$ and $95\%$ confidence levels for $w$ and $\Omega_m$ ($w$CDM model assumed) from WMAP9+SPT (red), CMASS (green), and WMAP9+SPT+CMASS (blue). The CMASS data break the degeneracy between $w$ and $\Omega_m$ constrained by CMB data.
• Figure 4: 2D marginalized contours for $68\%$ and $95\%$ confidence levels for $w$ and $\Omega_k$ (o$w$CDM model assumed) from WMAP9+SPT+CMASS (blue). While $w$ and $\Omega_k$ are not well constrained by WMAP9+SPT or CMASS-only, we only show the contour of $68\%$ confidence level from WMAP9+SPT (red). Adding the CMASS data on the CMB data improves the constraints on $w$ and $\Omega_k$ significantly, and the results are consistent with $w=-1$ and $\Omega_k=0$ ($\Lambda$CDM model).
• Figure 5: 2D marginalized contours for $68\%$ and $95\%$ confidence levels for $w$ and $f(z)\sigma_8(z)$ ($w$CDM model assumed) from CMB+$D_V(z)/r_s$ (thin solid red), CMB+$H(z) r_s$+$D_A(z)/r_s$CMASS(dashed blue). and CMB+$H(z) r_s$+$D_A(z)/r_s$+$f(z)\sigma_8(z)$ (thick solid black). One can see that there is no much improvement while replacing $D_V(z)/r_s$ with $H(z)r_s$+$D_A(z)/r_s$, but have significantly improvement on dark energy while adding $f(z)\sigma_8(z)$.