The Clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS): measuring growth rate and geometry with anisotropic clustering

TL;DR

The study uses anisotropic galaxy clustering from BOSS DR11 CMASS to jointly measure the growth rate fσ8 and the geometry of the universe via RSD and AP distortions. A streaming-model framework, validated with 600 PTHalo mocks, extracts Monopole and Quadrupole information to constrain D_V/r_d, F, and fσ8 at z ≈ 0.57, then combines these with Planck and BAO data to test ΛCDM-GR and explore deviations in curvature, dark energy, and gravity. The results are largely consistent with Planck-based ΛCDM-GR, yielding tight constraints on Ω_k, w, and the growth index γ, while revealing a mild preference for weaker gravity. The work strengthens low-redshift tests of cosmology and demonstrates the power of anisotropic clustering in constraining fundamental physics with current and future surveys.

Abstract

We use the observed anisotropic clustering of galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 CMASS sample to measure the linear growth rate of structure, the Hubble expansion rate and the comoving distance scale. Our sample covers 8498 ${\rm deg}^2$ and encloses an effective volume of 6.0 ${\rm Gpc}^3$ at an effective redshift of $\bar{z} = 0.57$. We find $fσ_8 = 0.441 \pm 0.044$, $H = 93.1 \pm 3.0\ {\mathrm{km}\ \mathrm{s}^{-1} \mathrm{Mpc}^{-1}}$ and $D_{\rm A} = 1380 \pm 23\ {\rm Mpc}$ when fitting the growth and expansion rate simultaneously. When we fix the background expansion to the one predicted by spatially-flat $Λ$CDM model in agreement with recent Planck results, we find $fσ_8 = 0.447 \pm 0.028$ (6 per cent accuracy). While our measurements are generally consistent with the predictions of $Λ$CDM and General Relativity, they mildly favor models in which the strength of gravitational interactions is weaker than what is predicted by General Relativity. Combining our measurements with recent cosmic microwave background data results in tight constraints on basic cosmological parameters and deviations from the standard cosmological model. Separately varying these parameters, we find $w = -0.983 \pm 0.075$ (8 per cent accuracy) and $γ= 0.69 \pm 0.11$ (16 per cent accuracy) for the effective equation of state of dark energy and the growth rate index, respectively. Both constraints are in good agreement with the standard model values of $w=-1$ and $γ= 0.554$.

Figures (19)

• Figure 1: The number density of CMASS DR11 galaxies in redshift bins of $\Delta z = 0.01$ in northern and southern Galactic hemispheres, computed assuming our fiducial cosmology.
• Figure 2: The two-dimensional correlation function of DR11 sample measured in bins of $1h^{-1}\times1h^{-1}$${\rm Mpc}^2$. We use first two Legendre multipoles of the correlation function in our study rather than the two-dimensional correlation function displayed here.
• Figure 3: The measured monopole and quadrupole of DR11 sample as a function of redshift-space separation $r$. The solid lines show predictions of our best-fitting model with $\Omega_\mathrm{b}h^2 = 0.0222$, $\Omega_\mathrm{m}h^2 = 0.1408$, $n_\mathrm{s} = 0.962$, $b\sigma_8=1.29$, $f\sigma_8=0.437$, $\alpha_\bot=1.017$, $\alpha_{||}=1.001$ and $\sigma^2_{\rm FOG}=12.6$.
• Figure 4: The reduced covariance matrix ($C_{i,j}/\sqrt{C_{i,i}C_{j,j}}$) of measured monopole and quadrupole in bins of 8$h^{-1}$ Mpc in the range $24h^{-1} < r < 152h^{-1}$ Mpc estimated from 600 PTHalo mocks. The $\xi_\ell$ measurements in neighbouring bins are strongly correlated.
• Figure 5: Histogram of the skewness of monopole and quadrupole measurements along with the expected distribution for a Gaussian variable. The empirical variance is compatible to the expectations from a Gaussian distribution.