The WiggleZ Dark Energy Survey: Improved Distance Measurements to z = 1
  with Reconstruction of the Baryonic Acoustic Feature
  We present significant improvements in cosmic distance measurements from the
WiggleZ Dark Energy Survey, achieved by applying the reconstruction of the
baryonic acoustic feature technique. We show using both data and simulations
that the reconstruction technique can often be effective despite patchiness of
the survey, significant edge effects and shot-noise. We investigate three
redshift bins in the redshift range 0.2<$z$<1, and in all three find
improvement after reconstruction in the detection of the baryonic acoustic
feature and its usage as a standard ruler. We measure model independent
distance measures $D_{\mathrm V}(r_{\mathrm s}^\mathrm{fid}/r_{\mathrm s})$ of
1716 $\pm$ 83 Mpc, 2221 $\pm$ 101 Mpc, 2516 $\pm$ 86 Mpc (68% CL) at effective
redshifts z = 0.44, 0.6, 0.73, respectively, where $D_{\mathrm V}$ is the
volume-average-distance, and $r_{\mathrm s}$ is the sound horizon at the end of
the baryon drag epoch. These significantly improved 4.8, 4.5 and 3.4 percent
accuracy measurements are equivalent to those expected from surveys with up to
2.5 times the volume of WiggleZ. These measurements are fully consistent with
cosmologies allowed by the analyses of the Planck Collaboration and the Sloan
Digital Sky Survey.We provide the $D_{\mathrm V}(r_{\mathrm
s}^\mathrm{fid}/r_{\mathrm s})$ posterior probability distributions and their
covariances. When combining these measurements with temperature fluctuations
measurements of Planck, the polarization of WMAP9, and the 6dF Galaxy Survey
baryonic acoustic feature, we do not detect deviations from a flat LCDM model.
Assuming this model we constrain the current expansion rate to $H_0$ = 67.15
$\pm$ 0.98 kms$^{-1}$Mpc$^{-1}$. Allowing the equation of state of dark energy
to vary we obtain $w_\mathrm{DE}$ = -1.080 $\pm$ 0.135. When assuming a curved
LCDM model we obtain a curvature value of $\Omega_{\mathrm K}$ = -0.0043 $\pm$
0.0047.
