SIMBAD references

The assumption that the Universe is homogeneous and isotropic on large scales is one of the fundamental postulates of cosmology. We have tested the large-scale homogeneity of the galaxy distribution in the Sloan Digital Sky Survey Data Release One (SDSS-DR1) using volume-limited subsamples extracted from the two equatorial strips that are nearly two-dimensional. The galaxy distribution was projected on the equatorial plane and we carried out a 2D multifractal analysis by counting the number of galaxies inside circles of different radii, r, in the range 5-150h^–1Mpc centred on galaxies. Different moments of the count-in-cells were analysed to identify a range of length-scales (60-70h^–1Mpc to 150h^–1Mpc), where the moments show a power-law scaling behaviour, and to determine the scaling exponent that gives the spectrum of generalized dimension D_q. If the galaxy distribution is homogeneous, D_q does not vary with q and is equal to the Euclidean dimension, which in our case is 2. We find that D_q varies in the range 1.7-2.2. We also constructed mock data from random, homogeneous point distributions and from lambda cold dark matter (ΛCDM)N-body simulations with bias b= 1, 1.6 and 2, and analysed these in exactly the same way. The values of D_q in the random distribution and the unbiased simulations show much smaller variations and these are not consistent with the actual data. The biased simulations, however, show larger variations in D_q and these are consistent with both the random and the actual data. Interpreting the actual data as a realization of a biased ΛCDM universe, we conclude that the galaxy distribution is homogeneous on scales larger than 60-70h^–1Mpc.