The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent
  Distance Measure at z=0.15
  We create a sample of spectroscopically identified galaxies with $z < 0.2$
from the Sloan Digital Sky Survey (SDSS) Data Release 7, covering 6813 deg$^2$.
Galaxies are chosen to sample the highest mass haloes, with an effective bias
of 1.5, allowing us to construct 1000 mock galaxy catalogs (described in Paper
II), which we use to estimate statistical errors and test our methods. We use
an estimate of the gravitational potential to "reconstruct" the linear density
fluctuations, enhancing the Baryon Acoustic Oscillation (BAO) signal in the
measured correlation function and power spectrum. Fitting to these
measurements, we determine $D_{V}(z_{\rm eff}=0.15) = (664\pm25)(r_d/r_{d,{\rm
fid}})$ Mpc; this is a better than 4 per cent distance measurement. This "fills
the gap" in BAO distance ladder between previously measured local and higher
redshift measurements, and affords significant improvement in constraining the
properties of dark energy. Combining our measurement with other BAO
measurements from BOSS and 6dFGS galaxy samples provides a 15 per cent
improvement in the determination of the equation of state of dark energy and
the value of the Hubble parameter at $z=0$ ($H_0$). Our measurement is fully
consistent with the Planck results and the $\Lambda$CDM concordance cosmology,
but increases the tension between Planck$+$BAO $H_0$ determinations and direct
$H_0$ measurements.
