ALBERT

Description: We present a simple and efficient phenomenological model for the two-dimensional two-point galaxy correlation function that works well over a wide range of scales, from large scales down to scales as small as 25 h –1 Mpc. Our model incorporates non-linear effects and a scale-dependent galaxy bias on small scales, and it allows the redshift-space distortions to be scale and direction dependent. We validate our model using LasDamas mock catalogues and apply it to the Sloan Digital Sky Survey (SDSS) Data Release Seven (DR7) luminous red galaxies (LRGs). Using only the monopole and quadrupole of the correlation function measured from the SDSS DR7 LRGs, we obtain improved measurements H ( z ) r s ( z d )/ c  = 0.0433 ± 0.0042, D A ( z )/ r s ( z d ) = 6.59 ± 0.46 and f ( z ) 8 ( z ) = 0.429 ± 0.089 at z  = 0.35, using the scale range 25 〈  s  〈 120 h –1 Mpc. We expect our results and model to be useful in tightening dark energy and gravity constraints from the full analysis of current and future galaxy clustering data.

Description: Galaxy clustering data can be used to measure the cosmic expansion history H ( z ), the angular diameter distance D A ( z ) and the linear redshift-space distortion parameter β( z ). Here we present a method for using effective multipoles of the galaxy two-point correlation function ( $\hat{\xi }_0(s)$ , $\hat{\xi }_2(s)$ , $\hat{\xi }_4(s)$ and $\hat{\xi }_6(s)$ , with s denoting the comoving separation) to measure H ( z ), D A ( z ) and β( z ), and validate it using LasDamas mock galaxy catalogues. Our definition of effective multipoles explicitly incorporates the discreteness of measurements, and treats the measured correlation function and its theoretical model on the same footing. We find that for the mock data, $\hat{\xi }_0+\hat{\xi }_2+\hat{\xi }_4$ captures nearly all the information, and gives significantly stronger constraints on H ( z ), D A ( z ) and β( z ), compared to using only $\hat{\xi }_0+\hat{\xi }_2$ . We apply our method to the sample of luminous red galaxies from the Sloan Digital Sky Survey Data Release 7 without assuming a dark energy model or a flat universe. We find that $\hat{\xi }_4(s)$ deviates on scales of s  〈 60 Mpc  h –1 from the measurement from mock data [in contrast to $\hat{\xi }_0(s)$ , $\hat{\xi }_2(s)$ and $\hat{\xi }_6(s)$ ]; thus, we only use $\hat{\xi }_0+\hat{\xi }_2$ for our fiducial constraints. We obtain { H (0.35), D A (0.35), m h 2 , β( z )} = {79.6 ${^{+ 8.3}_{- 8.7}}$ km s – 1 Mpc – 1 , 1057 ${^{+ 88}_{- 87}}$  Mpc, 0.103 ± 0.015, 0.44 ± 0.15} using $\hat{\xi }_0+\hat{\xi }_2$ . We find that H (0.35) r s ( z d )/ c and D A (0.35)/ r s ( z d ) [where r s ( z d ) is the sound horizon at the drag epoch] are more tightly constrained: { H (0.35) r s ( z d )/ c , D A (0.35)/ r s ( z d )} = {0.0437 ${^{+ 0.0041}_{- 0.0043}}$ ,6.48 ${^{+ 0.44}_{- 0.43}}$ } using $\hat{\xi }_0+\hat{\xi }_2$ .