Introduction

Cosmology is the attempt to build a coherent physical theory to explain the many and diverse observations of the universe at the largest scales. Statistical physics is concerned with the understanding of systems with many degrees of freedom. Clearly the second should therefore have much to say about and to contribute to the former. And indeed it does. Cosmology has, in particular in the development of its formalism since the 1970s borrowed tools from statistical physics. The mathematical language used to describe correlations in galaxy catalogs, for example, was imported from the theory of liquids. Direct exchange or even collaboration between people in the two communities has, however, been rare. Cosmology has thus tended to seek instruments when necessary from statistical physics, but has not been very much in contact with or influenced by the many developments which have taken place in statistical physics in the last decades. Statistical physics too - which has not hesitated to apply its methods even to many other fields outside physics (biology, geology, economics, ...) - has been relatively shy with respect to cosmology, despite the fact that this has become one of the most vibrant and exciting fields in contemporary science.

My research activity has its roots in a series of collaborations at the interface between statistical physics and cosmology, between researchers who belong to both communities, focusing on a range of problems in cosmology and gravitational dynamics approached with insights or methodologies coming from statistical physics. The specific issue which initiated this activity was the study of the clustering properties of galaxies as revealed by large redshift surveys, a context in which concepts of modern statistical physics (e.g. scale-invariance, fractality, ...) found a ready application. In recent years we have broadened considerably the range of problems in cosmology which we have addressed, treating in particular more theoretical issues about the statistical properties of standard cosmological models. In addition to the above mentioned topics, we are now considering the fashinating problmes related to the physics of systems with long range interactions and in paricular self-gravitating systems: formation of non-linear structures in gravitational N-body simulations and the formation of metastable stases.

What is common and original to all this activity, however, is that it is informed by a perspective and methodology which is that of statistical physics. Such interdisciplinary activity is an exciting playground for statistical physics, and one which can bring new and useful insights into cosmology.The study of the large scale structure of the universe is in an important and interesting stage characterized by a large increase of experimental data. In the near future such a tendency will be emphasized, for example, by new measurements of galaxy distribution (SDSS --- The Sloan Digital Sky Survey represents the most ambitious astronomical observational program ever undertaken) and of anisotropies of the cosmic microwave background radiation --- CMBR --- (Planck mission: Planck is the third Medium-Sized Mission (M3) of ESA's Horizon 2000 Scientific Program. It is designed to image the anisotropies of the CMBR field over the whole sky, with unprecedented sensitivity and angular resolution. Planck will provide a major source of information relevant to several cosmological and astrophysical issues, such as testing theories of the early universe and the origin of cosmic structure).

As in many other scientific areas, a statistical-mathematical filter is necessary to process data and obtain the correct information to be compared with theories and hypotheses. More specifically the methods of modern statistical physics, which have been successfully applied in many different fields, represent a new general framework for the understanding of cosmic structures, both from a phenomenological and theoretical point of views. On the one hand the clustering of matter in the universe is an important example of the fields in which scale invariance has been observed as a common and basic feature: power-law correlations have been detected both in the data of the galaxy distribution and in the outcome of numerical N-body simulations, although their origin is not yet understood. On the other hand the physics of scale-invariant and complex systems is a novel field which is including topics from several disciplines ranging from condensed matter physics to geology, biology, astrophysics and economics. This broad inter-disciplinary corresponds to the fact that these new ideas allow us to look at natural phenomena in a radically new and original way, eventually leading to unifying concepts independently of the detailed structure of the systems. The objective is the study of complex, scale-invariant structures, that appear both in space and time in the gravitational dynamics: New types of collective behaviors arise and their understanding represents one of the most challenging areas in modern statistical physics. In summary our research activity aim to apply the methods, concepts and ideas of modern statistical physics to the problem of cosmic structures developing a multidisciplinary approach to address longstanding challenges.