The Clustering of Galaxies in the SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Testing Deviations from $Λ$ and General Relativity using anisotropic clustering of galaxies

TL;DR

The paper tests the standard cosmological model by jointly analyzing geometry and growth from anisotropic galaxy clustering in the CMASS DR9 sample, exploiting RSD and AP effects to constrain dark energy and possible departures from GR. Using a CMASS DR9 $D_V$, $F$, and $f\sigma_8$ probe at $z=0.57$, complemented by CMB, SNeIa, and $H_0$ data, the authors obtain tight constraints on $\Omega_m$, curvature, and the DE equation of state, finding $w_0$ near $-1$ and small curvature. For deviations from GR, the growth parameter $\gamma$ is measured as $0.64\pm0.05$ (with full data), and MG-parameter fits like $\mu_1$ are constrained, with GR ($\gamma\approx0.55$, $\mu_1=0$) still broadly consistent within $2\sigma$. The results show that anisotropic clustering markedly improves DE constraints (by factors up to ~4 when combining with CMB) and overall remain consistent with $\Lambda$CDMGR, though mild hints of deviations persist at modest significance that future data could clarify.

Abstract

We use the joint measurement of geometry and growth from anisotropic galaxy clustering in the Baryon Oscillation Spectroscopic Survey Data Release 9 CMASS sample reported by Reid et al. to constrain dark energy properties and possible deviations from the General Relativity. Assuming GR and taking a prior on the linear matter power spectrum at high redshift from the cosmic microwave background (CMB), anisotropic clustering of the CMASS DR9 galaxies alone constrains $Ω_{\rm m} = 0.308 \pm 0.022$ and $100Ω_{\rm k} = 5.9 \pm 4.8$ for $w = -1$, or $w = -0.91 \pm 0.12$ for $Ω_k = 0$. When combined with the full CMB likelihood, the addition of the anisotropic clustering measurements to the spherically-averaged BAO location increases the constraining power on dark energy by a factor of 4 in a flat CDM cosmology with constant dark energy equation of state $w$ (giving $w = -0.87 \pm 0.05$). This impressive gain depends on our measurement of both the growth of structure and Alcock-Paczynski effect, and is not realised when marginalising over the amplitude of redshift space distortions. Combining with both the CMB and Supernovae Type Ia (SNeIa), we find $Ω_{\rm m} = 0.281 \pm 0.014$ and $1000Ω_{\rm k}=-9.2\pm5.0$ for $w = -1$, or $w_0 = -1.13 \pm 0.12$ and $w_{\rm a}=0.65 \pm 0.36$ assuming $Ω_k = 0$. Finally, when a $Λ$CDM background expansion is assumed, the combination of our estimate of the growth rate with previous growth measurements provides tight constraints on the parameters describing possible deviations from GR giving $γ= 0.64 \pm 0.05$. For one parameter extensions of the flat $Λ$CDM model, we find a $\sim 2σ$ preference either for $w > -1$ or slower growth than in GR. However, the data is fully consistent with the concordance model, and the evidence for these additional parameters is weaker than $2σ$.

Figures (13)

• Figure 1: The data points show the CMASS DR9 measurement of $f\sigma_8$ (circle) along with similar, low redshift, measurements (squares) and $1\sigma$ errorbars as presented in Table \ref{['table:fs8constraints']}. The three stripes show theoretical predictions for different gravity models allowing for uncertainty in the background cosmological parameters, constrained using only the WMAP 7 data Komatsu2011.
• Figure 2: The data points show recent measurements of $D_V$ (left panel, squares) and $F$ (right panel, squares) described in Table 1 along with latest measurements from CMASS DR9 data (circle) with $1\sigma$ errorbars. Red stripes show theoretical prediction of spatially-flat $\Lambda$CDM within the uncertainty in basic cosmological parameters as measured by WMAP 7 data; Blue stripes show theoretical predictions of Einstein-deSitter model within the uncertainty in $H_0$ as measured by HST key project riess:2011.
• Figure 3: The data points show some of the measurements presented in Table \ref{['table:fs8constraints']} with $1\sigma$ errorbars; the circle denotes the most recent CMASS DR9 measurement. The thick solid line shows the GR prediction, the thin solid lines show predictions for $\gamma =$ 0.45, 0.50, 0.60 and 0.65 (top to bottom), and the thin dashed lines show predictions for $\mu_1 =$ 0.2, 0.1, -0.1 and -0.2 (top to bottom). $\Omega_{\rm m}(z=0)$ and $\sigma_8$ at recombination are kept fixed to their WMAP7 best-fit values.
• Figure 4: The data points show the estimates of $f(z)\sigma_8(z)$, $D_{\rm V}/r_{\rm s}$ and $F$ from Reid12 with $1\sigma$ errorbars. Solid lines correspond to theoretical predictions for different values of $w_0$ when $w_{\rm a}$ and $\Omega_{\rm k}$ are set to zero while the distance to the last scattering surface and $\sigma_8$ at recombination are kept fixed to their wMAP7 best-fit values.
• Figure 5: Confidence levels ($1\sigma$ and $2\sigma$) for joint fits to parameters $\gamma$ and $\Omega_{\rm m}$. Solid lines show results for CMASS DR9 estimate of growth rate only, while dashed lines show results with previous estimates of growth rate added. In both cases the growth rate measurements are combined with CMB and SNeIa data. The dotted line shows the expected value in GR.