The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8

TL;DR

Beutler et al. analyze redshift-space distortions in the 2D correlation function of the 6dF Galaxy Survey to measure the growth of structure at very low redshift. They compare linear Kaiser predictions with non-linear extensions (streaming and Scoccimarro) and include wide-angle and Alcock-Paczynski considerations, extracting $g_\theta=f\sigma_8$ and $g_b=b\sigma_8$; with an $H_0$ prior they constrain $\sigma_8$ and $\Omega_m$, and combine with WMAP7 to estimate the growth index $\gamma$, finding results consistent with General Relativity. The low-$z$ nature of the data makes the measurement robust to fiducial cosmology and AP distortions, while the error analysis relies on jack-knife resampling validated by log-normal mocks. They forecast fsigma_8 constraints for future shallow surveys, highlighting WALLABY and TAIPAN as competitive probes that can complement high-redshift surveys in testing gravity and dark energy models.

Abstract

We present a detailed analysis of redshift-space distortions in the two-point correlation function of the 6dF Galaxy Survey (6dFGS). The K-band selected sub-sample which we employ in this study contains 81971 galaxies distributed over 17000deg^2 with an effective redshift z = 0.067. By modelling the 2D galaxy correlation function, xi(r_p,pi), we measure the parameter combination f(z)sigma_8(z) = 0.423 +/- 0.055. Alternatively, by assuming standard gravity we can break the degeneracy between sigma_8 and the galaxy bias parameter, b. Combining our data with the Hubble constant prior from Riess et al (2011), we measure sigma_8 = 0.76 +/- 0.11 and Omega_m = 0.250 +/- 0.022, consistent with constraints from other galaxy surveys and the Cosmic Microwave Background data from WMAP7. Combining our measurement of fsigma_8 with WMAP7 allows us to test the relationship between matter and gravity on cosmic scales by constraining the growth index of density fluctuations, gamma. Using only 6dFGS and WMAP7 data we find gamma = 0.547 +/- 0.088, consistent with the prediction of General Relativity. We note that because of the low effective redshift of 6dFGS our measurement of the growth rate is independent of the fiducial cosmological model (Alcock-Paczynski effect). We also show that our conclusions are not sensitive to the model adopted for non-linear redshift-space distortions. Using a Fisher matrix analysis we report predictions for constraints on fsigma_8 for the WALLABY survey and the proposed TAIPAN survey. The WALLABY survey will be able to measure fsigma_8 with a precision of 4-10%, depending on the modelling of non-linear structure formation. This is comparable to the predicted precision for the best redshift bins of the Baryon Oscillation Spectroscopic Survey (BOSS), demonstrating that low-redshift surveys have a significant role to play in future tests of dark energy and modified gravity.

Figures (13)

• Figure 1: The solid black line shows the 6dFGS redshift distribution, while the dashed black line shows one of the random mock catalogues containing the same number of galaxies. The blue solid and dashed lines show the distribution after weighting with $P_0 = 1600h^3\,$Mpc$^{-3}$ (see section \ref{['sec:dweight']} for more details on the employed weighting scheme).
• Figure 2: The 2D correlation function of 6dFGS using a density weighting with $P_0 = 1600h^3\,$Mpc$^{-3}$. For reasons of presentation we binned the correlation function in $0.5h^{-1}\,$Mpc bins, while in the analysis we use larger bins of $2h^{-1}\,$Mpc. Both redshift-space distortion effects are visible: the "finger-of-God" effect at small angular separation $r_p$, and the anisotropic (non-circular) shape of the correlation function at large angular separations.
• Figure 3: (a) The relative error in the 2D correlation function as a function of line-of-sight separation $\pi$ at a fixed $r_p = 11h^{-1}\,$Mpc. Other regions of the 2D correlation function behave in a similar manner. The solid lines show the Poisson error for different values of $P_0$, while the data points show the total (Poisson + sample variance) error obtained as the diagonal of the covariance matrix derived using jack-knife re-sampling. The purpose of the weighting ($P_0$) is to minimise the total error, which is achieved for a value of $P_0 \approx 1600h^{-3}\,$Mpc$^{3}$. The weighting reduces the error by almost a factor of two on most scales. The dashed line shows the error derived from log-normal realisations using $P_0 = 1600h^{-3}\,$Mpc$^{3}$ and is in very good agreement with the jack-knife error. (b) same as (a) for a fixed line-of-sight separation $\pi = 11h^{-1}\,$Mpc.
• Figure 4: The correlation matrix for the 2D correlation function $\xi(r_p,\pi)$ with a bin size of $2\times 2h^{-1}\,$Mpc. The upper-left corner shows the jack-knife estimate, while the lower-right corner shows the result of using $1500$ log-normal realisations. Since this plot shows the correlation of all $15\times 15$ bins it contains $225\times 225$ entries.
• Figure 5: This plot shows the correlation of bin $127$ ($r_p = 13h^{-1}\,$Mpc, $\pi = 17h^{-1}\,$Mpc) with all other bins in the 2D correlation function, derived using jack-knife re-sampling. It corresponds to row/column $127$ of the jack-knife correlation matrix which is shown in Figure \ref{['fig:cov2D']} (upper-left corner).