INTRODUCTION TO COSMOLOGY
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Delivery method
- Teaching methods
No specific prerequisites are required. Basic knowledge of the theory of General Relativity is needed, but this will be provided consistently during the course.
The exam will consist of a written test made up of 4 exercises to be performed in 3 hours and an oral test. At least 6 tests will be organized per academic year. The positive outcome of the written test is preliminary to the oral test.
As part of the written test, within each exercise it may also be required to provide some notion of theory or some theoretical demonstration. Each exercise will consist of several questions. In the written test, each exercise will be assigned a score (expressed in out of thirty) and explicitly indicated on the exam topic. The sum of the points assigned to each exercise will be 30/30. For the purposes of the evaluation of the written test, the following criteria will be considered, in order of priority:
1) the correctness and explanation of the procedures used to solve the problems;
2) the physical reliability of the results obtained;
3) the correctness of the calculations and of the final result in carrying out the same;
4) the correct use of technical terminology and units of measurement.
The written test will be considered positive with a mark higher than or equal to 16/30.
During the oral exam, the student will be questioned about the program. First, it will be asked to comment on any errors made in the written test. Then 4 or 5 questions relating to the content of the course will be asked to the student. In particular, some demonstrations and some calculations will be asked. The final grade will be assigned by making a weighted average of the assessments obtained in the written and oral tests. The weight assigned to the written test is 1/3, while that given to the oral exam is 2/3. The exam will be considered passed if the result of this weighted average is at least 18/30. To obtain honors, the student must produce a perfect written test and be able, during the oral exam, to answer questions with a high level of difficulty and to carry out non-trivial calculations.
The course aims to provide the fundamental knowledge of theoretical cosmology and observational cosmology.
Expected learning outcomes: At the end of the course, students will be able to:
- use the Robertson-Walker metric as a description of the geometry of the universe on large scales;
- apply thermodynamics and statistical mechanics in the early universe. In particular, to predict the abundance of light elements;
- understand what is meant by the hot "Big Bang" model, and how the cosmic background radiation is a consequence of it;
- understand the need for "dark" components in the universe: dark matter and dark energy;
- understand the process of formation of structures, in the linear regime, in an expanding universe.
The main contents of the course are as follows:
- Mathematical description of the expanding Universe, based on the theory of General Relativity;
- Thermal history of the Universe
- Cosmological perturbations
- Boltzmann equations
- Initial conditions
- Stochastic properties of cosmological perturbations
- Inflation
- Evolution of perturbations
- Anisotropies in the cosmic microwave background
- The expanding universe and its content
- The Olbers paradox
- The accelerated expansion of the universe and the Dark Energy
- Dark Matter
- Modern Cosmological Observations
- Open problems in cosmology
- The Friedmann – Lemaître – Robertson – Walker metric
- Friedmann's equations
- Distances in Cosmology - Thermal Equilibrium and Boltzmann Equation
- Formation of light nuclei in the Big Bang
- Recombination and Decoupling
- Thermal relics
- Cosmological perturbations
- Initial conditions for cosmological perturbations
- Power spectrum and Gaussian random fields
- Non-Gaussian perturbations
- Cosmological inflation
The lessons will be in presence, with presentation of the contents also with detailed execution of the calculations. There will be no lesson hours dedicated to exercises, but exercises will be carried out by the teacher and by the students during the course.