Characterizing the large scale inhomogeneity of the galaxy distribution

In order to investigate whether galaxy structures are compatible with the predictions of the standard LCDM cosmology, we focus here on the analysis of several simple and basic statistical properties of the galaxy density field. Namely, we test whether, on large enough scales (i.e., r>10 Mpc/h), this is self-averaging, uniform and characterized by a Gaussian probability density function of fluctuations. These are three different and clear predictions of the LCDM cosmology which are fulfilled in mock galaxy catalogs generated from cosmological N-body simulations representing this model. We consider some simple statistical measurements able to tests these properties in a finite sample. We discuss that the analysis of several samples of the Two Degree Field Galaxy Redshift Survey and of the Sloan Digital Sky Survey show that galaxy structures are non self-averaging and inhomogeneous on scales of ~100 Mpc/h, and are thus intrinsically different from LCDM model predictions. Correspondingly the probability density function of fluctuations shows a "fat tail" and it is thus different from the Gaussian prediction. Finally we discuss other recent observations which are odds with LCDM predictions and which are, at least theoretically, compatible with the highly inhomogeneous nature of galaxy distribution. We point out that inhomogeneous structures can be fully compatible with statistical isotropy and homogeneity, and thus with a relaxed version of the Cosmological Principle.Comment: 10 pages, 7 figures, to appear in the proceedings of the "Invisible Universe International Conference", AIP proceedings serie

Gravitational fluctuations of the galaxy distribution

We study the statistical properties of the gravitational field generated by galaxy distribution observed bythe Sloan Digital Sky Survey (DR7). We characterize the probability density function of gravitational force fluctuations and relate its limiting behaviors to the correlation properties of the underlying density field. In addition, we study whether the PDF converges to an asymptotic shape within sample volumes. We consider several volume-limited samples of the Sloan Digital Sky Survey and we compute the gravitational force probability density function (PDF). The gravitational force is computed in spheres of varying radius as is its PDF. We find that (i) the PDF of the force displays features that can be understood in terms of galaxy two-point correlations and (ii) density fluctuations on the largest scales probed, i.e. r~100 Mpc/h, still contribute significantly to the amplitude of the gravitational force. Our main conclusion is that fluctuations in the gravitational force field generated by galaxy structures are also relevant on scales ~ 100 Mpc/h. By assuming that the gravitational fluctuations in the galaxy distribution reflect those in the whole matter distribution, and that peculiar velocities and accelerations are simply correlated, we may conclude that large-scale fluctuations in the galaxy density field may be the source of the large-scale flows recently observed.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics. Version v2 matches the published pape

Fractal structures and the large scale distribution of galaxies

Galaxy structures are certainly fractal up to a certain crossover scale \lambda_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures are only discussed in terms of their global amplitude. Here we present a compact summary of these implications. First, we discuss the problem of the identification of the crossover scale \lambda_0 and the proper characterization of the scaling. We then consider the implications of these properties with respect to various physical phenomena and to the corresponding characteristic values, i.e. r_0, \sigma_8, \Omega, etc. These implications crucially depend on the value of \lambda_0, but they are still important for a relatively small value, say \lambda_0 \approx 50 \hmp. Finally we consider the main theoretical consequences of these results.Comment: 27 pages, 3 figures. To appear in the proceedings of the 7th Course in astrofundamental physics, Nato Advanced Study Institute, International Euroconference Erice, 5-16 December 199

Growth of correlations in gravitational N-body simulations

In the gravitational evolution of a cold infinite particle distribution, two-body interactions can be predominant at early times: we show that, by treating the simple case of a Poisson particle distribution in a static universe as an ensemble of isolated two-body systems, one may capture the origin of the first non-linear correlated structures. The developed power-law like behavior of the two-point correlation function is then simply related to the functional form of the time evolved nearest-neighbor probability distribution, whose time dependence can be computed by using Liouville theorem for the gravitational two-body problem. We then show that a similar dynamical evolution is also found in a large-scale ordered distribution, which has striking similarities to the case of a cosmological CDM simulation which we also consider.Comment: 15 pages, 28 figure