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4.2.4 General remarks

The basic scenario cannot be accepted without discussion. In the CDM model, in which small structures form first, it is predicted that at a large enough scale no structure should be encountered and that the density distribution should be completely random. This random distribution should be found at scales larger than about 30 Mpc. However, this might not be the case, as there is a large body of evidence suggesting a regular large structure forming a lattice at a larger scale. Broadhurst et al. (1990) found 10 periodic peaks separated by about 128 h-1Mpc in a pencil beam survey, which cannot be due to chance. Einasto et al. (1994) presented very clear evidence of a regular network with superclusters residing in chains separated by voids of diameters 100h-1Mpc. Such a regular lattice has also been confirmed by other authors (Tucker et al. 1997, Landy et al. 1996, Einasto et al. 1997 and others). Tully et al. (1992) compared the structure with a three dimensional chess-board. Similar regularity has been found in the distribution of QSO absorption-line systems (Quashnock et al. 1996) and in the CMB spectrum (Atrio-Barandela et al. 1997). The Tartu Group has been specially active in demonstrating this large-scale structure (Toomet et al. 1999).

Typical sizes of the lattice elements would be about 100-150 h-1Mpc, but the regularity in the alignment of these elements can be detected for much greater distances. In the Tully et al. (1992) supercluster distribution a straight line consisting of a chain of superclusters can be identified, from Tucana to Ursa Major, or even to Draco, in other words, a straight-line chain 700 h-1Mpc long. We will return to this point when discussing the cosmological magnetic field.

These observations have been rejected by many authors. The regularity found by Broadhurst et al. (1990) has not been found in other directions, but if a lattice is formed by filaments and voids, that is precisely what should be expected. Only in particular selected beams would a periodicity be detected. In the power spectrum of the Point Source Catalogue redshift survey (Sutherland et al. 1999) no periodicities, spikes or preferred directions were found. There was only the marginal evidence of a "step" in the power spectrum at k $ \sim$ 0.08hMpc-1, but this was just a 2$ \sigma$ effect that the authors considered a statistical fluctuation.

The possible crystal large scale structure is therefore under debate at present. Correlation function analysis is probably not appropriate to study a lattice of filaments and sheets, which would be somewhat deformable, elastic-like, due, for instance, to the gravity action caused by the largest superclusters. Other statistical methods to detect "foam lattices" should be developed. The evidence of a crystal-like structure for scales larger than about 100 Mpc is overwhelming.

Even if this possible observational fact were in complete contradiction with the hierarchical CDM models, strictly speaking, in practice, it would not invalidate them. It could be that, within a large structure ($ \sim$ 100 Mpc), the models would be available at a much shorter scale ($ \le$ 30 Mpc). Another explanation for the large scale should be sought, but the smaller scale models could remain valid. Current theoretical models, instead of an initial random distribution of $ \delta$, would start with a very large wide filament-sheet lattice as the initial condition. In practice, the existence of a large scale crystal is not incompatible with CDM models.

In addition, the hypothesis of a fractal universe without upper limits (Sylos-Labini, Monturi and Pietronero 1998) should be borne in mind.

Two quasi-philosophical criticisms can always be made of numerical models. If they assume a hypothesis and adjust a number of free parameters to agree with observations, the conclusion is that if the hypothesis is true, the set of free parameters proposed is correct, but the hypothesis has not been proved to be true. In the best case, the hypothesis is just compatible with observations. Furthermore, for N-body simulations, if we find results matching observational facts, we know that the physics used is able to explain these facts, but we are still unaware of the in-depth explanation.

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