We present the power spectrum of the reconstructed halo density fieldderived from a sample of luminous red galaxies (LRGs) from the SloanDigital Sky Survey (SDSS) Seventh Data Release (DR7). The halo powerspectrum has a direct connection to the underlying dark matter power fork <= 0.2hMpc-1, well into the quasi-linear regime. Thisenables us to use a factor of ~8 more modes in the cosmological analysisthan an analysis with kmax = 0.1hMpc-1, as wasadopted in the SDSS team analysis of the DR4 LRG sample. The observedhalo power spectrum for 0.02 < k < 0.2hMpc-1 is wellfitted by our model: χ2 = 39.6 for 40 degrees of freedomfor the best-fitting Λ cold dark matter (ΛCDM) model. Wefind Ωmh2(ns/0.96)1.2= 0.141+0.010-0.012 for a power-law primordialpower spectrum with spectral index ns andΩbh2 = 0.02265 fixed, consistent with cosmicmicrowave background measurements. The halo power spectrum alsoconstrains the ratio of the comoving sound horizon at the baryon-dragepoch to an effective distance to z = 0.35:rs/DV(0.35) =0.1097+0.0039-0.0042. Combining the halo powerspectrum measurement with the Wilkinson Microwave Anisotropy Probe(WMAP) 5 year results, for the flat ΛCDM model we findΩm = 0.289 +/- 0.019 and H0 = 69.4 +/-1.6kms-1Mpc-1. Allowing for massive neutrinos inΛCDM, we find eV at the 95 per cent confidence level. If weinstead consider the effective number of relativistic speciesNeff as a free parameter, we find Neff =4.8+1.8-1.7. Combining also with the Kowalski etal. supernova sample, we find Ωtot = 1.011 +/- 0.009and w = -0.99 +/- 0.11 for an open cosmology with constant dark energyequation of state w. The power spectrum and a module to calculate thelikelihoods are publicly available athttp://lambda.gsfc.nasa.gov/toolbox/lrgdr/.