The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z = 0.57 from anisotropic clustering

We analyse the anisotropic clustering of massive galaxies from the SloanDigital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS)Data Release 9 (DR9) sample, which consists of 264 283 galaxies in theredshift range 0.43 z 0.7 spanning 3275 deg². Bothpeculiar velocities and errors in the assumed redshift-distance relation('Alcock-Paczynski effect') generate correlations between clusteringamplitude and orientation with respect to the line of sight. Togetherwith the sharp baryon acoustic oscillation (BAO) standard ruler, ourmeasurements of the broad-band shape of the monopole and quadrupolecorrelation functions simultaneously constrain the comoving angulardiameter distance (2190 ± 61 Mpc) to z = 0.57, the Hubbleexpansion rate at z = 0.57 (92.4 ± 4.5 km s^-1Mpc^-1) and the growth rate of structure at that same redshift(dσ₈/d ln a = 0.43 ± 0.069). Our analysisprovides the best current direct determination of both D_A andH in galaxy clustering data using this technique. If we further assume aΛcold dark matter expansion history, our growth constrainttightens to dσ₈/d ln a = 0.415 ± 0.034. Incombination with the cosmic microwave background, our measurements ofD_A, H and dσ₈/d ln a all separately requiredark energy at z > 0.57, and when combined implyΩ_Λ = 0.74 ± 0.016, independent of theUniverse's evolution at z 0.57. All of these constraints assumescale-independent linear growth, and assume general relativity tocompute both O(10 per cent) non-linear model corrections and our errors.In our companion paper, Samushia et al., we explore further cosmologicalimplications of these observations.