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 200 000 blue galaxies in a cosmic volume of \sim 1 h ^ { -3 } Gpc ^ { 3 } .
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 r ^ { 3 } within 1 per cent , or equivalently the fractal dimension of the sample is within 1 per cent of D _ { 2 } = 3 , at radii larger than 71 \pm 8 h ^ { -1 } Mpc at z \sim 0.2 , 70 \pm 5 h ^ { -1 } Mpc at z \sim 0.4 , 81 \pm 5 h ^ { -1 } Mpc at z \sim 0.6 , and 75 \pm 4 h ^ { -1 } Mpc at z \sim 0.8 .
We demonstrate the robustness of our results against selection function effects , using a \Lambda CDM N -body simulation and a suite of inhomogeneous fractal distributions .
The results are in excellent agreement with both the \Lambda CDM N -body simulation and an analytical \Lambda CDM prediction .
We can exclude a fractal distribution with fractal dimension below D _ { 2 } = 2.97 on scales from \sim 80 h ^ { -1 } Mpc up to the largest scales probed by our measurement , \sim 300 h ^ { -1 } Mpc , at 99.99 per cent confidence .