87972 - Quantum Cosmology

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 (Hot Big Bang) and their shortcomings; Raychaudhuri equations and approach to the "Big Bang" singularity; brief review homogenous (Bianchi) metrics;

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

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

4) canonical quantisation of cosmological models and conditions for the semiclassical limit (background field approximation) via the Born-Oppenheimer approach;

5) basics of quantisation of matter fields and metric perturbations in curved background;

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.

 

Readings/Bibliography

Textbooks and review articles will be suggested during the lessons.

Notes of the course are available on "Virtuale" and will be updated during the lesson period.

Teaching methods

Standard lectures with blackboard.

Assessment methods

Final examination at a date fixed by appointment with the teacher.

The test consists of a written essay on a topic of your choice, to be send by email to the teacher prior to the exam date, and oral examination about the essay and topics covered during the course.

Teaching tools

Blackboard.

Office hours

See the website of Roberto Casadio

See the website of Francisco Manuel Soares Verissimo Gil Pedro