  We apply a new model for the spherically averaged correlation function at
large pair separations to the measurement of the clustering of luminous red
galaxies (LRGs) made from the SDSS by Cabre and Gaztanaga(2009). Our model
takes into account the form of the BAO peak and the large scale shape of the
correlation function. We perform a Monte Carlo Markov chain analysis for
different combinations of datasets and for different parameter sets. When used
in combination with a compilation of the latest CMB measurements, the LRG
clustering and the latest supernovae results give constraints on cosmological
parameters which are comparable and in remarkably good agreement, resolving the
tension reported in some studies. The best fitting model in the context of a
flat, Lambda-CDM cosmology is specified by Omega_m=0.261+-0.013,
Omega_b=0.044+-0.001, n_s=0.96+-0.01, H_0=71.6+-1.2 km/s/Mpc and
sigma_8=0.80+-0.02. If we allow the time-independent dark energy equation of
state parameter to vary, we find results consistent with a cosmological
constant at the 5% level using all data sets: w_DE=-0.97+-0.05. The large scale
structure measurements by themselves can constrain the dark energy equation of
state parameter to w_DE=-1.05+-0.15, independently of CMB or supernovae data.
We do not find convincing evidence for an evolving equation of state. We
provide a set of "extended distance priors" that contain the most relevant
information from the CMB power spectrum and the shape of the LRG correlation
function which can be used to constrain dark energy models and spatial
curvature. Our model should provide an accurate description of the clustering
even in much larger, forthcoming surveys, such as those planned with NASA's
JDEM or ESA's Euclid mission.
