87972 - Quantum Cosmology

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

At the end of the course the student will have a comprehensive knowledge of modern theoretical models of the primordial universe in the framework of the quantum theory of fields and general relativity. All topics will be taught with a critical perspective that takes into account cosmological data. The student will be able to analyse and compare specific models and observational evidence to discriminate among different scenarios.

Course contents

The course will cover the following topics:

1) Brief review of the simplest cosmological models stemming from the cosmological principle of homogeneity and isotropy and their shortcomings; Raychaudhuri equations and approach to the "Big Bang" singularity; inhomogenous Kasner metrics;

2) introduction to inflationary models for the very early Universe to solve the problems of the Big Bang model and shortcomings of the semiclassical approach in the very early Universe;

3) general covariance and diffeomorphism invariance of the gravitational and matter actions in Lagrangian and Hamiltonian formalism; Hamiltonian and momentum constraints in the Einstein gravity;

4) general theory of constrained systems and canonical quantisation for the Einstein gravity; the Wheeler-deWitt equation;

5) canonical quantisation of cosmological models and conditions for the semiclassical limit via the Born-Oppenheimer approach;

6) general theory of linear cosmological perturbations; the Cosmic Microwave Backgroung radiation in inflationary models;

7) exit from the inflationary phase and reheating;

8) brief introduction to the LambdaCDM model for the late Universe; the problems of dark energy and dark matter.



Textbooks and review articles will be suggested during the lessons.

Teaching methods

Standard lectures with blackboard.

Assessment methods

The test consists of a final oral exam, fixed by appointment with the teacher, with the presentation of a written essay on a topic of your choice, and free questions from the teacher on other topics covered in the course.

Teaching tools


Office hours

See the website of Roberto Casadio

See the website of Gianmassimo Tasinato