Using Multipoles of the Correlation Function to Measure H(z), D_A(z),
  and \beta(z) from Sloan Digital Sky Survey Luminous Red Galaxies
  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 (\xi_0(s), \xi_2(s),
\xi}_4(s), and \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,
\xi_0+\xi_2+\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
\xi_0+\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 \xi}_4(s) deviates on scales of
s<60Mpc/h from the measurement from mock data (in contrast to \xi_0(s),
\xi_2(s), and \xi_6(s)), thus we only use \xi_0+\xi_2 for our fiducial
constraints. We obtain {H(0.35), D_A(0.35), Omega_mh^2, beta(z)} =
{79.6_{-8.7}^{+8.3} km/s/Mpc, 1057_{-87}^{+88}Mpc, 0.103\pm0.015, 0.44\pm0.15}
using \xi_0+\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 \xi_0+\xi_2.
