  The anisotropic galaxy clustering on large scales provides us with a unique
opportunity to probe into the gravity theory through the redshift-space
distortions (RSDs) and the Alcock-Paczynski effect. Using the multipole power
spectra up to hexadecapole (ell=4), of the Luminous Red Galaxy (LRG) sample in
the data release 7 (DR7) of the Sloan Digital Sky Survey II (SDSS-II), we
obtain simultaneous constraints on the linear growth rate f, angular diameter
distance D_A, and Hubble parameter H at redshift z = 0.3. For this purpose, we
first extensively examine the validity of a theoretical model for the
non-linear RSDs using mock subhalo catalogues from N-body simulations, which
are constructed to match with the observed multipole power spectra. We show
that the input cosmological parameters of the simulations can be recovered well
within the error bars by comparing the multipole power spectra of our
theoretical model and those of the mock subhalo catalogues. We also carefully
examine systematic uncertainties in our analysis by testing the dependence on
prior assumption of the theoretical model and the range of wavenumbers to be
used in the fitting. These investigations validate that the theoretical model
can be safely applied to the real data. Thus, our results from the SDSS DR7 LRG
sample are robust including systematics of theoretical modeling; f(z = 0.3)
sigma_8(z = 0.3) =0.49+-0.08(stat.)+-0.04(sys.), D_A (z = 0.3)
=968+-42(stat.)+-17(sys.)[Mpc], H (z = 0.3)
=81.7+-5.0(stat.)+-3.7(sys.)[km/s/Mpc]. We believe that our method to constrain
the cosmological parameters using subhaloes catalogues will be useful for more
refined samples like CMASS and LOWZ catalogues in the Baryon Oscillation
Spectroscopic Survey in SDSS-III.
