Large-scale Cosmic Homogeneity from a Multifractal Analysis of the PSCz Catalogue

We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSCz sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D_2=2.992(3) for r>30 h^{-1} Mpc. This provides strong evidence in favour of a Universe which obeys the Cosmological Principle.