  We measure the large-scale real-space power spectrum P(k) using luminous red
galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement
to sharpen constraints on cosmological parameters from the Wilkinson Microwave
Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation
method using Pseudo-Karhunen-Loeve eigenmodes, producing uncorrelated
minimum-variance measurements in 20 k-bands of both the clustering power and
its anisotropy due to redshift-space distortions, with narrow and well-behaved
window functions in the range 0.01h/Mpc < k < 0.2h/Mpc. Results from the LRG
and main galaxy samples are consistent, with the former providing higher
signal-to-noise. Our results are robust to omitting angular and radial density
fluctuations and are consistent between different parts of the sky. They
provide a striking confirmation of the predicted large-scale LCDM power
spectrum.
  Combining only SDSS LRG and WMAP data places robust constraints on many
cosmological parameters that complement prior analyses of multiple data sets.
The LRGs provide independent cross-checks on Om and the baryon fraction in good
agreement with WMAP. Within the context of flat LCDM models, our LRG
measurements complement WMAP by sharpening the constraints on the matter
density, the neutrino density and the tensor amplitude by about a factor of
two, giving Omega_m=0.24+-0.02 (1 sigma), sum m_nu < 0.9 eV (95%) and r<0.3
(95%). Baryon oscillations are clearly detected and provide a robust
measurement of the comoving distance to the median survey redshift z=0.35
independent of curvature and dark energy properties. Within the LCDM framework,
our power spectrum measurement improves the evidence for spatial flatness,
sharpening the curvature constraint Omega_tot=1.05+-0.05 from WMAP alone to
Omega_tot=1.003+-0.010. Assuming Omega_tot=1, the equation of state parameter
is constrained to w=-0.94+-0.09, indicating the potential for more ambitious
future LRG measurements to provide precision tests of the nature of dark
energy. All these constraints are essentially independent of scales k>0.1h/Mpc
and associated nonlinear complications, yet agree well with more aggressive
published analyses where nonlinear modeling is crucial.
