Complexity in cosmic structures Francesco Sylos Labini Enrico Fermi Center & Institute for Complex Systems (ISC-CNR) Rome Italy A.Gabrielli, FSL, M. Joyce, L. Pietronero Statistical physics for cosmic structures Springer Verlag 2005

Early times density fields COBE DMR, 1992 WMAP satellite 2006

Late times density fields 300 Mpc/h (2006) 150 Mpc/h (1990) 5 Mpc/h

The problem of cosmological structure formation Initial conditions: Uniform distribution (small amplitude fluctuations) Dynamics: infinite self-gravitating system Final conditions: Stronlgy clustered, power-law correlations

What do we know about dark matter ? Cosmological energy budget: the “standard model” Non baryonic dark matter (e.g. CDM): -never detected on Earth -needed to make structures compatible with anisotropies Dark Energy -never detected on Earth -needed to explain SN data What do we know about dark matter ? Fundamental and observational constraints

Classification of uniform structures Substantially Poisson (finite correlation length) Gas Super-Poisson (infinite correlation length) Critical system Extremely fine-tuned distributions Sub-Poisson (ordered or super-homogeneous) HZ tail

Problem at large angular scales CMBR: results CMBR Problem at large angular scales P(k) = k --> C l(l+1) = const Gravitational effect Angular correlation function vanishes at > 60 deg (COBE/WMAP teams and Schwartz et al. 2004) Small quadrupole/octupole (COBE/WMAP teams)

Extendend Classification of homogeneous structures Statistically isotropic and homogeneous Super-homogeneous Poisson-like Critical Fractals: isotropic but not homogeneous

Conditional correlation properties

Galaxy correlations: results Sylos Labini, F., Montuori M. & Pietronero L. Phys Rep, 293, 66 (1998) Hogg et al. (SDSS Collaboration). ApJ, 624, 54 (2005)

From order to complex structures: Discrete gravitational N body problem From order to complex structures: A Toy model Gravitational Dynamics generates Complex Structures Power law correlations Non Gaussian velocity distributions Probability distributions with “fat tails” (In)dipendence on IC and universal properties….

Structure formation: the cosmological problem

Homogeneity scale: not yet identified in galaxy distributions Summary HZ tail: the only distinctive feature of FRW-IC in matter distribution is the behavior of the large scales tail of the real space correlation function Note yet observed in galaxy distributions Problem with large angle CMBR anisotropies Homogeneity scale: not yet identified in galaxy distributions Structures in N-Body simulations: too small and maybe different in nature from galaxy structures Basic propeerties of SGS