# Ph.D. Thesis

## Out-of-equilibrium dynamics of self-gravitating systems in cosmology

The formation of structures in the Universe is one of the major questions in cosmology. The growth of structures in the linear regime of low amplitude fluctuations is well understood analytically, but *N*-body simulations remain the main tool to probe the *non-linear* regime where fluctuations are large. We study this question approaching the problem from the more general perspective to the usual one in cosmology, that of statistical physics. Indeed, this question can be seen as a well posed problem of out-of-equilibrium dynamics of systems with long-range interaction. In this context, it is natural to develop simplified models to improve our understanding of this system, reducing the question to fundamental aspects. We define a class of infinite *1-d* self-gravitating systems relevant to cosmology, and we observe strong qualitative similarities with the evolution of the analogous *3-d *systems. We highlight that the spatial clustering which develops may have scale invariant (fractal) properties, and that they display *self-similar* properties in their temporal evolution. We show that the measured exponents characterizing the scale-invariant clustering can be very well accounted for using an appropriately generalized *stable-clustering* hypothesis. Further by means of an analysis in terms of *halo* selected using a *friend-of-friend* algorithm, we show that, in the corresponding spatial range, structures are statistically virialized. Thus the non-linear clustering in these *1-d* models corresponds to the development of a *virialized fractal hierarchy*. We conclude with a separate study which formalizes a classification of pair-interactions based on the convergence properties of the forces acting on particles as a function of system size, rather than the convergence of the potential energy, as it is usual in statistical physics of long-range interacting systems.

*last update: May 2018*