The clustering of galaxies in the SDSS-III Baryon Oscillation
  Spectroscopic Survey: Evolution of higher-order correlations demonstrated
  with Minkowski Functionals
  We probe the higher-order galaxy clustering in the final data release (DR12)
of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS)
using germ-grain Minkowski Functionals (MFs). Our data selection contains
$979,430$ BOSS galaxies from both the northern and southern galactic caps over
the redshift range $z=0.2 - 0.6$. We extract the higher-order part of the MFs,
detecting the deviation from the purely Gaussian case with $\chi^2 \sim
\mathcal{O}(10^3)$ on 24 degrees of freedom across the entire data selection.
We measure significant redshift evolution in the higher-order functionals for
the first time. We find $15-35\%$ growth, depending on functional and scale,
between our redshift bins centered at $z=0.325$ and $z=0.525$. We show that the
structure in higher order correlations grow faster than that in the two-point
correlations, especially on small scales where the excess approaches a factor
of $2$. We demonstrate how this trend is generalizable by finding good
agreement of the data with a hierarchical model in which the higher orders grow
faster than the lower order correlations. We find that the non-Gaussianity of
the underlying dark matter field grows even faster than the one of the galaxies
due to decreasing clustering bias. Our method can be adapted to study the
redshift evolution of the three-point and higher functions individually.
