Statistical physics for complex cosmic structures

Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a new perspective in the field which can be tested by the many new data which are appearing in the near future. In particular, galaxy structures show fractal correlation up to the present observational limits. The cosmic microwave background radiation, which should trace the initial conditions from which these structures have emerged through gravitational dynamics, is instead extremely smooth. Understanding the relation between the complex galaxy structures and the smooth microwave background radiation represents an extremely challenging problem in the field of structure formation.