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 lar ge-scale fractal behaviour in this catalogue. We find the correlation dimen sion 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 exte nd the analysis out to much larger scales. We find firm evidence that the s ample becomes homogeneous at large scales; the correlation dimension of the sample is D-2=2.992 +/-0.003 for r > 30 h(-1) Mpc. This provides strong ev idence in favour of a universe that obeys the cosmological principle.