Fractal structure and self-organization Research Activity
Our research activity includes several different subjects.While in the past we have mostly focused on the comprehension of the statistical properties of galaxy large scale structures and its theoretical implications, in recent times we have investigated also N-Body simulations of gravitational clustering and theoretical models.
i) Data analysis, Galaxy Structures: We analyze publicly available galaxy catalogs and compute especially the fractal dimension of the galaxy distribution. We have found that galactic structures are fractal with dimension up to a distance scale of ~ [1]. The homogeneity scale of at which can not be determined from presently available catalogs [2] (see also the web page
http://pil.phys.uniroma1.it/debate.html).ii) N-body simulations: From the point of view of statistical mechanics, it is very hard to study the properties of infinite systems of self-gravitating particles. This is mainly due to the long range nature of gravitational interaction, which cannot be shielded by the balance of charges with opposite sign, as e.g. in a plasma. Therefore all scales contribute to the potential energy of a particle. We work on this problem with N-body simulations and analytical tools. In a first step initiated by the Rome group, we have studied the formation of structure from purely random initial conditions (Poisson noise) [3]. We have investigated the statistical properties of cosmological N-body simulations based on CDM-like models, showing that they develop structures which are almost independent of initial conditions and cosmological parameters [4, 5]. A detailed study of gravitational clustering via N-body simulation is being performed in collaboration with Prof. R. Durrer and T. Baertschiger (Geneva), Dr. F. Sylos Labini (Geneva and Paris) Prof. Pietronero, M. Bottaccio and A. Gabrielli (Roma), M. Joyce and B.Jancovici (Paris) and J. Lebowitz (Rutgers, USA).
iii) Interpretation and Modeling : We also study discrete realizations of the Harrison Zel'dovich initial conditions predicted by cosmological inflation and observed in the anisotropies of the cosmic microwave background. We have shown that these initial conditions correspond to 'super-homogeneous', glass-like correlation properties of galaxies [6].
This work is in progress now, and we (the Geneva group) collaborate with M. Joyce and B. Jancovici (Paris), L. Pietronero and A. Gabrielli (Rome) and J. Lebowitz (Rutgers, USA).
References
1. Sylos Labini F., Montuori M., Pietronero L., Physics Reports, 293, 66, (1998).
2. Joyce M. and Sylos Labini F. Astrophys. J. Lett. 554, L1, (2001).
3. L. Pietronero, M. Bottaccio, M. Montuori, F. Sylos Labini 'Scaling in cosmic structures', in the Proceedings of the International Workshop on Scaling and Disordered Systems, Fractals, in press (2002).
4. T. Baertschiger and F. Sylos Labini 'On the problem of initial conditions in cosmological N-body simulations' Europhys. Lett. 57, 322-328 (2002).
5. T. Baertschiger, M. Joyce and F. Sylos Labini, Submitted to Phys. Rev. Lett. (2002).
6. A. Gabrielli, M. Joyce, and F. Sylos Labini,'The Glass-like Universe : Real-space correlation properties of standard cosmological models' Physical Review D, in press (scheduled issue: 15 April 2002).
