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

WMAP satellite 2006

COBE DMR, 1992

150 Mpc/h(1990)

300 Mpc/h(2006)

5 Mpc/h

Late times density fields

The problem of cosmological structure formation

Initial conditions: Uniform distribution (small amplitude fluctuations)

Final conditions: Stronlgy clustered,

power-law correlations

Dynamics: infinite self-gravitating system

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

Substantially Poisson (finite correlation length)

Super-Poisson (infinite correlation length)

Sub-Poisson (ordered or super-homogeneous)

Classification of uniform structures

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<ΔM(r)2 > <∝ M(r) >

< M(r) >∝ r3

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<ΔM(r)2 > <∝ M(r) >β 1 < β < 2

Extremely fine-tuned distributions

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<ΔM(r)2 > <∝ M(r) >β

2/3 < β <1 < ΔM(r)2 >∝ r2

Gas

Critical system

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σφ2(r) ≈ const.

HZ tail

CMBR: results

Angular correlation function vanishes at > 60 deg (COBE/WMAP teamsand Schwartz et al. 2004)

Small quadrupole/octupole (COBE/WMAP teams)

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<ΔM 2(r) >≈ r2 ⇒ C(l) ≈ l(l +1)[ ]−1

Super-homogeneous

Poisson-like

Critical

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< n >=< n(r) >p= const

Statistically isotropic and homogeneous

Fractals: isotropic but not homogeneous

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< n(r) >p ≈ r−γ

< n >= 0

Extendend Classification of homogeneous structures

Conditional correlation properties

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N(r)P

= N i(r) = BrDi=1

M

∑ 0 < D ≤ 3

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n(r)P

=N(r)

p

V (r)= 3B

4πrD−3

Galaxy correlations: results

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

Discrete gravitational N body problem

From order to complex structures:A Toy model

GravitationalDynamics

generates

Complex Structures

Power law correlationsNon Gaussian velocity distributionsProbability distributions with “fat tails”(In)dipendence on IC and universal properties….

Structure formation: the cosmological problem

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