Recovering the topology of the initial density fluctuations using the IRAS Point Source Catalogue Redshift Survey

We apply the reconstruction technique of Nusser & Dekel to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the non-Gaussianities that are expected to develop in the mild non-linear regime of gravitational evolution. We study the evolution of isodensity contours defined using an adaptive smoothing algorithm, in order to minimize the problems derived from the non-commutativity of the smoothing operator and the time-evolution operator. We study the topology of these isodensity contours and concentrate on the evolution of the amplitude drop of the genus compared to a Gaussian field with an identical power spectrum, in order to quantify the level of phase-correlation present in the field. In order to test the method and to quantify the level of statistical uncertainty, we apply the method to a set of mock PSCz catalogues derived from the N -body simulations of two standard cold dark matter (CDM) models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the correct amplitude drops. When applied to PSCz, the level of phase correlations observed is very low on all scales ranging from 5 to 60  h ⁻¹ Mpc, providing support to the theory that structure originated from Gaussian initial conditions.