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 \beta ( 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 \beta ( z ) , and validate it using LasDamas mock galaxy catalogs .
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 \beta ( z ) , compared to using only \hat { \xi } _ { 0 } + \hat { \xi } _ { 2 } .

We apply our method to the sample of luminous red galaxies ( LRGs ) from the Sloan Digital Sky Survey ( SDSS ) Data Release 7 ( DR7 ) 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 from the measurement from mock data ( in contrast to \hat { \xi } _ { 0 } ( s ) , \hat { \xi } _ { 2 } ( s ) , and \hat { \xi } _ { 6 } ( s ) ) , leading to a significant difference in the measured mean values of H ( z ) , D _ { A } ( z ) , and \beta ( z ) from \hat { \xi } _ { 0 } + \hat { \xi } _ { 2 } and \hat { \xi } _ { 0 } + \hat { \xi } _ { 2 } + \hat { \xi } _ { 4 } , thus it should not be used in deriving parameter constraints .
We obtain \ { H ( 0.35 ) ,D _ { A } ( 0.35 ) , \Omega _ { m } h ^ { 2 } , \beta ( z ) \ } = \ { 79.6 _ { -8.7 } ^ { +8.3 } { km } { s } ^ { -1 } { Mpc } ^ { -1 } , 1057 _ { -87 } ^ { +88 } Mpc , 0.103 \pm 0.015 , 0.44 \pm 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 _ { -0.0043 } ^ { +0.0041 } , 6.48 _ { -0.43 } ^ { +0.44 } \ } using \hat { \xi } _ { 0 } + \hat { \xi } _ { 2 } .
We conclude that the multipole method can be used to isolate systematic uncertainties in the data , and provide a useful cross-check of parameter measurements from the full correlation function .