D1. Knowledge and understanding: At the end of the course, the student must demonstrate knowledge of the fundamental principles of cosmology and the formation and evolution of cosmic structures at various scales. In particular, they must deepen their study of the evolution of cosmological perturbations in various regimes and for different scenarios, learn the main observables that theoretical model predictions are compared against, and understand how such comparisons constrain the cosmological models themselves. D2. Ability to apply knowledge and understanding: At the end of the course, the student must be able to apply the knowledge acquired in D1 to understand how different observations in cosmology constrain various models of Dark Matter and Dark Energy, the geometry of the Universe, and the behavior of gravity on cosmological scales. D3. Autonomy of judgment: At the end of the course, the student will be able to judge the basic methods for understanding the implications of both observational and theoretical results, obtained from analytical derivations and numerical simulations. D4. Communication skills: At the end of the course, the student must be able to clearly explain the concepts acquired in D1, describe the various causal mechanisms that influence the evolution of cosmic structures, describe what cosmological information is derived from various observables, and be proficient in deriving the necessary formulas and equations for these purposes. D5. Learning ability: At the end of the course, the student must be able to independently deepen their understanding of the topics covered and be able to master the concepts learned to undertake a potential thesis in cosmology or extragalactic astrophysics, whether of a theoretical/numerical or observational nature.

Knowledge from previous courses of Physics (Thermodynamics, Statistical Mechanics, Relativity, Quantum Mechanics) and of Astrophysics (Cosmology I, Observational Cosmology, Radiative Processes, Astrophysics of Galaxies) are required.

1. Introduction to the course with references to observational results and ongoing and future cosmological experiments. 2. Notes on the thermal history of the Universe: decoupling and freeze-out of dark matter particles. 3. Cosmological perturbations in the Newtonian regime and notes on relativistic perturbations: isentropic and isocurvature perturbations, linear solutions, Jeans scale, Meszaros effect, free-streaming scale, baryonic oscillations, transfer function. 4. Description of the non-linear gravitational collapse of a collisionless fluid: Lagrangian approach and Zeldovich approximation; the spherical collapse model; hierarchical clustering and self-similar scaling. Methods for cosmological numerical simulations: N-body methods (direct codes, particle-mesh, tree) and hydrodynamic methods (Eulerian methods; Lagrangian/SPH methods); generation of initial conditions. 5. Measurements of the cosmic density field and statistical methods: the filtered fluctuation field, variance, correlation functions; Gaussian random fields; statistics of cosmic velocity fields and redshift space distortions. 6.Gravitational lensing effects: lensing formalism, lensing equation,time-delay, deflection angle, the concept of magnification, the convergence field and shear; strong lensing and weak lensing; reconstruction of the gravitational potential from lensing. 7. Formation and structure of dark matter halos and their statistical properties: the mass function (derivation with the Press-Schechter method, the excursion set method, the distribution of progenitors and the merger tree); the correlation function of halos and halo bias; the halo model for clustering in the non-linear regime.

1. H. Mo, F. van den Bosch & S.D.M. White: Galaxy Formation and Evolution, Cambridge University Press, 2010 2. R. Narayan & M. Bartelmann: Gravitational lensing (Eds. A. Dekel and J.P. Ostriker. Cambridge : Cambridge University Press, 1999., p.360, astro-ph/9606001 3. S.D.M. White: Formation and evolution of galaxies, Lectures at the Les HouchesSummer School, astro-ph/9410093 4. J. Binney & S. Tremaine: Galactic Dynamics, 1987, Princeton University Press 5. W. Hu: Lecture Notes on CMB Theory, arXiv:0802.3688

https://moodle2.units.it/course/view.php?id=14324

Blackboard presentation, complemented by the projection of slides. Exercises to be carried out outside classes, concerning the argument of the class lectures, that require the coding of simple programs in a language of choice of the student.

Any changes to the methods described here, which may be necessary to ensure the application of the safety protocols related to any emergency situations, will be communicated in the Department, Study Program and teaching website.

The oral exam may be held in Italian or English, at the student's choice. The oral exam, structured in the form of an interview, involves covering a minimum of three topics, the first of which is chosen by the student, and lasts on average about 30/35 minutes. The purpose is to assess the student's level of knowledge of the program's topics, the level of mastery of the specialized language, and the ability to develop reasoning by coherently connecting topics covered in different parts of the program.