  The complex relationship between the galaxy density field and the underlying
matter field limits our ability to extract cosmological constraints from galaxy
redshift surveys. Our approach is to use halos rather than galaxies to trace
the underlying mass distribution. We identify Fingers-of-God (FOGs) and replace
multiple galaxies in each FOG with a single halo object. This removes the
nonlinear contributions of satellite galaxies, the one-halo term. We test our
method on a large set of high-fidelity mock SDSS Luminous Red Galaxy (LRG)
catalogs. We find that the aggressive FOG compression algorithm adopted in the
LRG P(k) analysis of Tegmark et al. (2006) leads to a ~10% correction to the
underlying matter power spectrum at k = 0.1 h/Mpc and ~40% correction at k=0.2
h/Mpc, thereby compromising the cosmological constraints. In contrast, the
power spectrum of our reconstructed halo density field deviates from the
underlying matter power spectrum by less than 1% for k less than 0.1 h/Mpc and
less than 4% for k less than 0.2 h/Mpc. The reconstructed halo density field
also removes the bias in the measurement of the redshift space distortion
parameter beta induced by the FOG smearing of the linear redshift space
distortions.
