Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N- body simulations of two cold dark matter (CDM) cosmogonies, an Einstein-de Sitter model (tau CDM) and a flat model with Ohm (0) = 0.3 and a cosmologic al constant (Lambda CDM). We use these to assess the significance of the ap parent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observ ers to create mock catalogues with the geometry and the distance distributi on of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our tau CDM (Lambda CDM) simulation. A couple of large clum ps in a catalogue can produce a high peak at low wavenumbers in the corresp onding one-dimensional power spectrum, without any apparent large-scale per iodicity in the original redshift histogram. Although the simulated redshif t histograms frequently display regularly spaced clumps, the spacing of the se clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a tau CDM (Lambda CDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced c lumps with a significance as high as that of the real data. We conclude tha t in CDM universes, the regularity on a scale of similar to 130 h(-1) Mpc o bserved by Broadhurst et al. has a priori probability well below 10(-3).