The Relativistic Universe

Contact: Pr. Christian Marinoni


What's up there in the sky that may shed light on fundamental physics? This is the question around which this course is organized. After reviewing some fundamental aspects of general  relativity,  we will present  the physical principles of the standard model of cosmology. The goal is to understand the key features of the large-scale structure of space-time : its   geometry, energy content and  dynamics. To this purpose we will study cosmic symmetries and conservation principles, we will solve Einstein field equations in the presence of fluids of different nature, and we will determine the relativistic kinematics of particles in a moving background.   Once the formalism is set up,  we will  explore the physics at work during  the  various stages of cosmic evolution, paying  special attention to describe the primordial inflationary phase and the dark energy phase. Notably, we will exploit these two puzzling phenomena as a pretext to explore eventual departures from the general relativistic theory of gravity, such as the existence of extra-dimensions or of additional scalar degrees of freedom. The most conspicuous portion of the course will be devoted to present relativistic perturbation theory, the gravitational paradigm that allows to understand how   large-scale structures of the universe, such as galaxies, grew out of small initial energy fluctuations of quantum nature.   We will show what theory tells us about the spatial arrangement of matter and energy in the cosmos and we will contrast predictions against available empirical evidences. The goal is to present evidences supporting the standard model, point to critical aspects that are still at stake and lively debated in the field, as well as discuss crucial predictions that still need to be confirmed. On the methodological side, we will provide the students with the basic conceptual and mathematical tools  for eventually  contributing to this discovery process.


Lecture material is displayed on the chalkboard and discussed in dynamical interaction with the students. This will allow  interspersing conceptual presentations with practical exercitations, ideally facilitating the assimilation process.  Handouts containing exercises and problems will be distributed on a weekly basis so that students can continuously monitor their level of comprehension.   Lecture notes, deepening and completing the subjects covered in class, will also be available.  Cosmology uses methods from nearly all fields of physics, among which are general relativity, statistical physics, nuclear and atomic physics, particle physics and field theory. We will not assume preliminary knowledge in any specialized field. Indeed, with very few exceptions,  the derivation of every formula begins with basic physical principles. Of course some knowledge of general relativity, differential geometry and particle physics would be helpful, but this is not a necessary condition for understanding the lectures.



1. S. Weinberg, Gravitation and Cosmology,  John Wiley & Sons (1972),
2. V. Muckhanov, Physical fundations of Cosmology,  Cambridge University. Press (2005),
3. D.S. Gorbunov & V. A. Rubakov, Introduction to the theory of the universe, World scientific (2011)
4. D.S. Gorbunov & V. A. Rubakov, Cosmological perturbations and inflationary Theory , World scientific (2011)
5. P. Peter &  J.-P. Uzan, Primordial  Cosmology, Oxford University Press   (2005),
6. S. M. Carrol, Spacetime and Geometry, Addison Wesley (2004)