The complex universe: recent observations and theoretical challenges

Abstract

The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical characterization of these structures shows that galaxy distribution is inhomogeneous in these samples, being characterized by large-amplitude fluctuations of large spatial extension. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales as 1/r. At larger scales, the density depends only weakly (logarithmically) on the system size and density fluctuations follow the Gumbel distribution of extreme value statistics. These complex behaviors are different from what is expected in a homogeneous distribution with Gaussian fluctuations. The observed density inhomogeneities pose a fundamental challenge to the standard picture of cosmology but it also represent an important opportunity which points to new directions with respect to many cosmological puzzles. Indeed, the fact that matter distribution is not uniform, in the limited range of scales sampled by observations, rises the question of understanding how inhomogeneities affect the large-scale dynamics of the universe. We discuss several attempts which try to model inhomogeneities in cosmology, considering their effects with respect to the role and abundance of dark energy and dark matter.

30 pages, 10 figures

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• Exact solution to the averaging problem in cosmology
• Living in a Void: Testing the Copernican Principle with Distant Supernovae
• Global fluctuations and Gumbel statistics
• Absence of self-averaging and of homogeneity in the large scale galaxy distribution
• Finite-size scaling in extreme statistics
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• Gravitational energy and cosmic acceleration
• Persistent fluctuations in the distribution of galaxies from the Two degree Field Galaxy Redshift Survey
• Extension and estimation of correlations in Cold Dark Matter models

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• Violation of the FRW consistency condition as a signature of backreaction
• Backreaction and FRW consistency conditions
• Cosmological networks
• Evaluating backreaction with the ellipsoidal collapse model
• The fractal cosmological model
• Thermodynamics of gravitational clustering phenomena: $N$-body self-gravitating gas on the sphere ${\mathbb{S}}^3\subset {\mathbb{R}}^4$
• Single Past Null Geodesic in the Lemaitre-Tolman-Bondi Cosmology
• Analytic Form of a Two-Dimensional Critical Distribution
• On physical vacuum as an unobservable system