Recovering the Topology of the Initial Density Fluctuations Using the   IRAS Point Source Catalogue Redshift Survey
  We apply the reconstruction technique of Nusser & Dekel (1992) to the recently available Point Source Catalogue Redshift Survey (PSCz) in order to subtract the phase correlations 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-comutivity of operators. We study the genus curves of the fields thus obtained and concentrate on the evolution of the amplitude drops, a meta-statistic able 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' CDM models, kindly granted to us by the Virgo consortium. We find the method to be reliable in recovering the right amplitude drops. When applied to PSCz, the level of phase correlations observed is very low on all scales ranging from 5h-1Mpc to 60 h-1Mpc, providing support to the theory that structure originated from gaussian initial conditions. 
A. Canavezes (CAUP,Portugal), J Sharpe (Imperial College,UK)