2012MNRAS.425..116S

We have made the largest volume measurement to date of the transition to large-scale homogeneity in the distribution of galaxies. We use the WiggleZ survey, a spectroscopic survey of over 200000 blue galaxies in a cosmic volume of ∼ 1h^–3Gpc³. A new method of defining the `homogeneity scale' is presented, which is more robust than methods previously used in the literature, and which can be easily compared between different surveys. Due to the large cosmic depth of WiggleZ (up to z = 1), we are able to make the first measurement of the transition to homogeneity over a range of cosmic epochs. The mean number of galaxies N(< r) in spheres of comoving radius r is proportional to r³ within 1per cent, or equivalently the fractal dimension of the sample is within 1per cent of D₂= 3, at radii larger than 71±8h^–1Mpc at z ∼ 0.2, 70±5h^–1Mpc at z ∼ 0.4, 81±5h^–1Mpc at z ∼ 0.6 and 75±4h^–1Mpc at z ∼ 0.8. We demonstrate the robustness of our results against selection function effects, using a Λ cold dark matter (ΛCDM) N-body simulation and a suite of inhomogeneous fractal distributions. The results are in excellent agreement with both the ΛCDM N-body simulation and an analytical ΛCDM prediction. We can exclude a fractal distribution with fractal dimension below D₂ = 2.97 on scales from ∼ 80h^–1Mpc up to the largest scales probed by our measurement, ∼ 300 h^–1Mpc, at 99.99per cent confidence.