1. 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

2. Early times density fields
COBE DMR, 1992
WMAP satellite 2006

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

4. 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

5. 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

6. 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

7. 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)

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

9. Conditional correlation properties

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

11. 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….

12. Structure formation: the cosmological problem

13. 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