We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two Cold Dark Matter cosmogonies , an Einstein-de Sitter model ( \tau CDM ) and a flat model with \Omega _ { 0 } = 0.3 and a cosmological constant ( \Lambda CDM ) .
We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al .
( 1990 ) .
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 observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al .
data .
We produce 1936 ( 2625 ) quasi-independent catalogues from our \tau CDM ( \Lambda CDM ) simulation .
A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum , without any apparent large-scale periodicity in the original redshift histogram .
Although the simulated redshift histograms frequently display regularly spaced clumps , the spacing of these clumps varies between catalogues and there is no ‘ preferred ’ period over our many realisations .
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 clumps with a significance as high as that of the real data .
We conclude that in CDM universes , the regularity on a scale of \sim 130 h ^ { -1 } Mpc observed by Broadhurst et al .
has a priori probability well below 10 ^ { -3 } .