Author: Carolina Saggiomo

Cosmology (COSMO)

Academic Team

Course Content

Type: Compulsory– PEC&AC Track – 2nd Trimester

This course provides a comprehensive introduction to modern cosmology, covering the theoretical framework, observational evidence, and open questions about the origin, evolution, and large-scale structure of the Universe.

Main Topics

  • Cosmological principles and the Friedmann–Lemaître–Robertson–Walker models.
  • Thermal history of the Universe: from the hot Big Bang to the matter and radiation eras.
  • Inflation and the generation of cosmic perturbations.
  • Baryogenesis and Big Bang nucleosynthesis.
  • Cosmic microwave background and large-scale structure formation.
  • Formation of the first stars and galaxies.
  • Observational cosmology: distance measurements, standard candles, and large surveys.
  • Gravitational waves in cosmology.
  • Computational methods for simulating cosmic evolution.
  • Open problems: dark matter, dark energy, and alternatives to the standard model.

Skills Acquired

  • Interpret and apply theoretical models of cosmic evolution.
  • Relate observational data to cosmological parameters.
  • Analyze the interplay between theory, simulations, and astronomical observations.

Lecture notes

     •      Introduction

     •      History & Principles

     •      Friedmann-Robertson-Walker Models

     •      The Thermal History of the Universe

     •      Big Bang Nucleosynthesis

     •      Inflation

     •      Gauge Invariant Perturbations + Baryogenesis  

     •      Cosmic Microwave Background Radiation:

                –      observations

                –      theory

     •      The Large-Scale Structure of the Universe

     •      Cosmic Dawn: The First Stars & Galaxies

     •      Observational Cosmology:

                –      the distance ladder

                –      CMB & surveys

     •      Gravitational Waves

     •      Computational Cosmology

     •      Open Problems in Cosmology:

                –      the CDM crisis

                –      alternative gravity

– supplementary notes on Inflation, GIP and Baryogenesis by Juan Garcia-Bellido

– annotated notes created by MSc students from the year 2020/21 can be found under Links

Note: All the course information is available on its website.

Teaching Plan Information

Course Schedule

Gravitation (GRA)

Academic Team

Course Content

Type: Compulsory– PEC&AC Track – 1stTrimester

This course offers an in-depth study of gravity as described by Einstein’s General Theory of Relativity. Students will explore gravity as a geometric property of spacetime, learn to derive and interpret exact solutions to Einstein’s equations, and understand their cosmological and astrophysical relevance.

Main Topics

  • Foundations of General Relativity: equivalence principles, covariance, and differential geometry.
  • Einstein’s field equations: vacuum and matter solutions, weak field limits, and exact metrics like Schwarzschild, Reissner-Nordström, and Kerr.
  • Experimental tests of General Relativity and classical Solar System tests.
  • Introduction to black hole physics, including singularities, event horizons, and black hole mechanics.
  • Gravitational waves: theory, emission, and modern detection methods.
  • Astrophysical applications: black hole mergers and supermassive black holes in galaxies.

Skills Acquired

  • Understand gravity as a geometric effect on spacetime structure.
  • Derive and analyze key exact solutions of Einstein’s equations.
  • Relate theory with experimental and observational tests.
  • Gain insight into current research topics like gravitational waves and black hole astrophysics.

Reading List

  • Lecture Notes on General Relativity by Daniel Baumann (all sections except Section 7 on Cosmology).

Additional Recommended Books:

  • Sean M. Carroll, Spacetime and Geometry
  • James Hartle, Gravity
  • Bernard Schutz, A First Course in Relativity
  • Ray d’Inverno, Introducing Einstein’s Relativity
  • M. P. Hobson et al., General Relativity
  • Anthony Zee, Einstein Gravity in a Nutshell
  • Robert M. Wald, General Relativity
  • Steven Weinberg, Gravitation and Cosmology
  • P. A. M. Dirac, General Theory of Relativity
  • Misner, Thorne & Wheeler, Gravitation
  • Eric Poisson & Clifford Will, Gravity
  • Yvonne Choquey-Bruhat, Introduction to General Relativity

Course Outline:

  • Special Relativity: Lorentz transformations, spacetime, relativistic kinematics and dynamics
  • Gravity as Geometry: equivalence principle, curved spacetime
  • Differential Geometry basics: manifolds, tensors, metric
  • Geodesics: equations, Newtonian limit, applications (Mercury precession, light bending)
  • Spacetime Curvature: covariant derivatives, Riemann tensor, geodesic deviation
  • Einstein Equations: field equations, matter, cosmological constant, vacuum solutions
  • Gravitational Waves: linearized gravity, wave creation
  • Black Holes: Schwarzschild, charged, rotating

Teaching Plan Information

Course Schedule