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)/dln (1 + z) from redshift space measurements of the 3D anisotropic galaxy two-point correlation ξ(z), but the degeneracy of its transverse (or projected) component with galaxy bias b, i.e. ξ_⊥(z) ∝ D²(z)b²(z), introduces large errors in the growth measurement. Here, we present a comparison between two methods which breaks 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 catalogues 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 the second- and third-order galaxy correlations without the need of modelling matter correlations. For haloes with masses lower than 10¹⁴ h^-1 M_⊙, we find 10 per cent 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.