A 2% Distance to z=0.35 by Reconstructing Baryon Acoustic Oscillations -
  I : Methods and Application to the Sloan Digital Sky Survey
  We apply the reconstruction technique to the clustering of galaxies from the
SDSS DR7 LRG sample, sharpening the baryon acoustic oscillation (BAO) feature
and achieving a 1.9% measurement of the distance to z=0.35. This is the first
application of reconstruction of the BAO feature in a galaxy redshift survey.
We update the reconstruction algorithm of Eisenstein et al, 2007 to account for
the effects of survey geometry as well as redshift-space distortions and
validate it on 160 LasDamas simulations. We demonstrate that reconstruction
sharpens the BAO feature in the angle averaged galaxy correlation function,
reducing the nonlinear smoothing scale \Sigma_nl from 8.1 Mpc/h to 4.4 Mpc/h.
Reconstruction also significantly reduces the effects of redshift-space
distortions at the BAO scale, isotropizing the correlation function. This
sharpened BAO feature yields an unbiased distance estimate (< 0.2%) and reduces
the scatter from 3.3% to 2.1%. We demonstrate the robustness of these results
to the various reconstruction parameters, including the smoothing scale, the
galaxy bias and the linear growth rate. Applying this reconstruction algorithm
to the SDSS LRG DR7 sample improves the significance of the BAO feature in
these data from 3.3 sigma for the unreconstructed correlation function, to 4.2
sigma after reconstruction. We estimate a relative distance scale D_V/r_s to
z=0.35 of 8.88+/-0.17, where r_s is the sound horizon and D_V = (D_A^2/H)^{1/3}
is a combination of the angular diameter distance D_A and Hubble parameter H.
Assuming a sound horizon of 154.25 Mpc, this translates into a distance
measurement D_V (z=0.35) = 1.356+/-0.025 Gpc. We find that reconstruction
reduces the distance error in the DR7 sample from 3.5% to 1.9%, equivalent to a
survey with three times the volume of SDSS.
