We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15 000 galaxies over 84.1 per cent of the sky, and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N‐body simulations of four variants of the cold dark matter (CDM) cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random‐phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 to 32 h−1 Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. When scaled to a common normalization, the amplitude drop depends primarily on the shape of the power spectrum. We find that the constant‐bias standard CDM model can be ruled out at high significance, because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large‐scale power all fit the PSCz data almost equally well, with a slight preference for a high‐density τCDM model.

A B S T R A C TWe use the PSCz IRAS galaxy redshift survey to analyse the cosmological galaxy dipole out to a distance of 300 h 21 Mpc. The masked area is filled in three different ways, first by sampling the whole sky at random, secondly by using neighbouring areas to fill a masked region, and thirdly using a spherical harmonic analysis. The method of treatment of the mask is found to have a significant effect on the final calculated dipole.The conversion from redshift space to real space is accomplished by using an analytical model of the cluster and void distribution, based on 88 nearby groups, 854 clusters and 163 voids, with some of the clusters and all of the voids found from the PSCz data base.The dipole for the whole PSCz sample appears to have converged within a distance of 200 h 21 Mpc and yields a value for b V 0X6 ab 0X75 0X11 20X08 , consistent with earlier determinations from IRAS samples by a variety of methods. For b 1Y the 2s range for V 0 is 0.43±1.02.The direction of the dipole is within 138 of the cosmic microwave background (CMB) dipole, the main uncertainty in direction being associated with the masked area behind the Galactic plane. The improbability of further major contributions to the dipole amplitude coming from volumes larger than those surveyed here means that the question of the origin of the CMB dipole is essentially resolved.

In this paper, we pursue a new technique to search for evidence of a finite universe, making use of a spherical Mexican Hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales, we test whether compact orientable flat topologies are consistent with the COBE–DMR data. We consider topological sizes ranging from half to twice the horizon size. A scale–scale correlation test indicates that non‐trivial topologies with appropriate topological sizes are as consistent with the COBE–DMR data as an infinite universe. Among the finite models, the data seems to prefer a universe which is about the size of the horizon for all but the hypertorus and the triple‐twist torus. For the latter, the wavelet technique does not seem a good discriminator of scales for the range of topological sizes considered here, while a hypertorus has a preferred size which is 80 per cent of the horizon. This analysis allows us to find a best fit topological size for each model, although cosmic variance might limit our ability to distinguish some of the topologies.

We use the Least Action Principle to predict the peculiar velocities of PSCz galaxies inside cz=2000 km s(-1). Linear theory is used to account for tidal effects to cz=15 000 km s(-1), and we iterate galaxy positions to account for redshift distortions. As the Least Action Principle is valid beyond linear theory, we can predict reliable peculiar velocities even for very nearby galaxies (i.e., cz less than or equal to 500 km s(-1)). These predicted peculiar velocities are then compared with the observed velocities of 12 galaxies with Cepheid distances. The combination of the PSCz galaxy survey (with its large sky coverage and uniform selection) with the accurate Cepheid distances makes this comparison relatively free from systematic effects. We find that galaxies are good tracers of the mass, even at small (less than or equal to 10 h(-1) Mpc) scales; under the assumption of no biasing, 0.25 less than or equal to beta less than or equal to0.75 (at 90 per cent confidence). We use the reliable predicted peculiar velocities to estimate the Hubble constant H-0 from the local volume without 'stepping up' the distance ladder, finding a confidence range of 65-75 km s(-1) Mpc(-1) (at 90 per cent confidence)