Measuring the growth of matter fluctuations with third-order galaxy
  correlations
  Measurements of the linear growth factor $D$ at different redshifts $z$ are
key to distinguish among cosmological models. One can estimate the derivative
$dD(z)/d\ln(1+z)$ from redshift space measurements of the 3D anisotropic galaxy
two-point correlation $\xi(z)$, but the degeneracy of its transverse (or
projected) component with galaxy bias $b$, i.e. $\xi_{\perp}(z) \propto\ D^2(z)
b^2(z)$, introduces large errors in the growth measurement. Here we present a
comparison between two methods which break this degeneracy by combining second-
and third-order statistics. One uses the shape of the reduced three-point
correlation and the other a combination of third-order one- and two-point
cumulants. These methods use the fact that, for Gaussian initial conditions and
scales larger than $20$ $h^{-1}$Mpc, the reduced third-order matter
correlations are independent of redshift (and therefore of the growth factor)
while the third-order galaxy correlations depend on $b$. We use matter and halo
catalogs from the MICE-GC simulation to test how well we can recover $b(z)$ and
therefore $D(z)$ with these methods in 3D real space. We also present a new
approach, which enables us to measure $D$ directly from the redshift evolution
of second- and third-order galaxy correlations without the need of modelling
matter correlations. For haloes with masses lower than $10^{14}$
$h^{-1}$M$_\odot$, we find $10%$ deviations between the different estimates of
$D$, which are comparable to current observational errors. At higher masses we
find larger differences that can probably be attributed to the breakdown of the
bias model and non-Poissonian shot noise.
