Large-scale periodicity and Gaussian fluctuations

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Abstract
We propose a strategy for evaluating the theoretical implications of large-scale ‘periodicity’ in deep pencil-beam redshift surveys. Given at present the observed galaxy distribution along one long pencil (NGP+ SGP), we search for statistics that would be as effective as possible in ruling out theoretical models. In order to obtain meaningful conclusions, these a posteriori statistics should eventually be applied as a priori statistics to future pencils of comparable length. At the present stage, the most discriminatory statistics are found to be those in which centres of ‘superclusters’ are identified along the pencil and ‘periodicity’ is measured in the distribution of these centres with equal weights. When the observed NGP+SGP pencil is considered to its full, two-sided length, such statistics rule out a Poisson distribution of clusters at the > 99.9 per cent confidence level, suggesting a large-scale origin for ‘periodicity’. Trying to rule out the whole standard family of models that assume isotropic Gaussian fluctuations, we confront the data with an extreme representative of this family, in which a characteristic scale of ∼ 100 h−1 Mpc has been built into the power spectrum (this is the natural cosmological scale if Ω ∼ 0.1). We generate a randomphased realization of such a spectrum, evolve it in time, identify ‘galaxies’ and count them along randomly oriented long pencils. Even with our most discriminatory statistics, these Gaussian pencils are as ‘periodic’ as the NGP+SGP pencil a few per cent of the time. This is not enough to rule out Gaussian fluctuations with high confidence. However, if a few more independent two-sided pencils of similar length are observed to score similarly under the same statistics, then Gaussian fluctuations will be rejected with high confidence. Moreover, a cubic-lattice toy model scores similarly to the Gaussian model, indicating that no homogeneous cosmology would permit several ∼ 1800 h−1 Mpc pencils as periodic as the NGP+SGP pencil.

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