  We present the power spectrum of the reconstructed halo density field derived
from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey
Seventh Data Release (DR7). The halo power spectrum has a direct connection to
the underlying dark matter power for k <= 0.2 h/Mpc, well into the quasi-linear
regime. This enables us to use a factor of ~8 more modes in the cosmological
analysis than an analysis with kmax = 0.1 h/Mpc, as was adopted in the SDSS
team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo
power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6
for 40 degrees of freedom for the best fit LCDM model. We find \Omega_m h^2 *
(n_s/0.96)^0.13 = 0.141^{+0.009}_{-0.012} for a power law primordial power
spectrum with spectral index n_s and \Omega_b h^2 = 0.02265 fixed, consistent
with CMB measurements. The halo power spectrum also constrains the ratio of the
comoving sound horizon at the baryon-drag epoch to an effective distance to
z=0.35: r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}. Combining the halo power
spectrum measurement with the WMAP 5 year results, for the flat LCDM model we
find \Omega_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for
massive neutrinos in LCDM, we find \sum m_{\nu} < 0.62 eV at the 95% confidence
level. If we instead consider the effective number of relativistic species Neff
as a free parameter, we find Neff = 4.8^{+1.8}_{-1.7}. Combining also with the
Kowalski et al. (2008) supernova sample, we find \Omega_{tot} = 1.011 +/- 0.009
and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation
of state w.
