Measuring the transition to homogeneity with photometric redshift surveys

We study the possibility of detecting the transition to homogeneity using photometric redshift catalogues. Our method is based on measuring the fractality of the projected galaxy distribution, using angular distances, and relies only on observable quantities. It thus provides a way to test the cosmological principle in a model-independent unbiased way. We have tested our method on different synthetic inhomogeneous catalogues and shown that it is capable of discriminating some fractal models with relatively large fractal dimensions, in spite of the loss of information due to the radial projection. We have also studied the influence of the redshift bin width, photometric redshift errors, bias, non-linear clustering, and surveyed area on the angular homogeneity index H-2(theta) in a Lambda cold dark matter cosmology. The level to which an upcoming galaxy survey will be able to constrain the transition to homogeneity will depend mainly on the total surveyed area and the compactness of the surveyed region. In particular, a Dark Energy Survey (DES)-like survey should be able to easily discriminate certain fractal models with fractal dimensions as large as D-2 = 2.95. We believe that this method will have relevant applications for upcoming large photometric redshift surveys, such as DES or the Large Synoptic Survey Telescope.