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General Relativity & Cosmology

General Relativity:
- Provide the basic concepts and tools to describe gravitational phenomena in terms of the geometry of space-time.
- Explain how the metric tensor and the principles of Relativity determine the trajectories of test particles.
- Explain how the matter distribution determines the properties of the metric tensor.
- Present the main predictions of General Relativity.
- Present modern tests able to discriminate between the various theories of gravity.

- Provide a general overview of the history of the Universe.
- Explain in more detail the theory of the most important cosmological processes.
- Present the recent observations, their results and implications for cosmology.
- Discuss open theoretical questions and future experiments.

Syllabus : " General Relativity & Cosmology "

- Lectures 30 hours, Tutorials 20 hours (2nd Semester) -

(R├ęza Ansari, Bartjan van Tent, Robin Zegers)

Chapter 1: General Relativity
Equivalence principle, gravity and the geometry of space-time.
Propagation in curved space-times and geodesics.
Covariant derivatives, curvature tensor, Einstein’s equation.
Testing the predictions of General Relativity: planetary orbits, binary systems, black holes.

Chapter 2: Cosmology - Theory and Observations
Expansion of the Universe, its thermal history, and the standard cosmological model.
Nucleosynthesis and cosmological implications from particle physics.
Primordial inflation and the theory of cosmological fluctuations.
Theory and observations of the cosmic microwave background and of the large-scale structure of the Universe.
Dark matter & dark energy - theoretical questions and observational evidence (e.g. baryon acoustic oscillations, weak lensing).

Recommended textbooks:

  • Gravity, An Introduction to Einstein’s General Relativity, J. B. Hartle
  • A First Course in General Relativity, B. F. Schutz
  • An Introduction to Modern Cosmology, A. Liddle

Course prerequisites and corequisites

This course is considered an introduction to the subject. As such it does not require much prior knowledge. It only requires basic notions of the Lagrangian formulation of classical mechanics, of Special Relativity, and of thermodynamics.

No corequisites are necessary. It is nevertheless recommended to follow the Major "Particles, Nuclei and Universe", which contains several complementary notions. It is also recommended to follow the Major "Advanced Statistical and Quantum mechanics" to be able to relate General Relativity to the theories of matter fields.

Course concrete goals

On completion of the course students should be able to:

— Understand that gravitational phenomena, such as planetary orbits, Mercury’s perihelion advance, the bending of light rays, gravitational collapse, and the cosmological expansion, should all be described in terms of the curvature of space-time
— Master the basic tools allowing us to describe these phenomena and to make predictions
— Understand how General Relativity relates to Special Relativity and the theory of Electromagnetism
— Have a good knowledge of the thermal history of the Universe and the processes that play a role there, as well as the standard cosmological model and the observational evidence that supports it
— Be able to perform basic calculations in several areas of modern cosmology
— Be aware of the open questions and future experiments in cosmology.