General relativity and applications to cosmology

Description

A] Introduction to general relativity:
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-- Gravity as a manifestation of curved spacetime : Einstein’s equivalence principle.
-- Trajectories on a static and spherically-symmetric spacetime : Mercury’s perihelion and deflection of light.
-- General covariance : tensors and their covariant derivatives, usual theories in curved spacetime.
-- Dynamical spacetime : Riemann and Ricci tensors, Einstein’s equations.
-- Vacuum solutions : black holes.
-- Wave solutions : gravitational waves.

B] Introduction to cosmology:
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-- Cosmological principle : Friedmann-Lemaître-Robertson-Walker spacetime, comoving observers and redshift.
-- Expanding universes : Friedmann equations, cosmological fluids.
-- Big Bang theory : our universe, dark matter and dark energy.
-- Thermal history of the universe : CMB, BBN, neutrinos.
-- Cosmological inflation.
-- A word on cosmological perturbations (only if times allows).

Compétences requises

-- Knowing special relativity and variational principles (e.g., four-vectors, Minkowski metric, proper time, Einstein’s summation, Euler-Lagrange equations) will help, although they will be briefly reviewed during the course.

Compétences visées

•    Applying knowledge in physics

•    Apply methods from mathematics and digital technology

•    Produce a critical analysis, with hindsight and perspective

•    Research a physics topic using specialised resources

•    Communicate in writing and orally, including in English

•    Contribute to research work in physics

•    Respect ethical, professional and environmental principles in the practice of physics

Informations complémentaires

-- Theoretical course given at the board.
-- Exercises and their corrections will be provided, but will not be treated in class.
-- 3h-long written exam. Goal : testing a basic conceptual and technical understanding. Notes taken in class, corrections of exercises, summaries made at home, etc, are welcome.

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