Author: Carolina Saggiomo

Academic Team

Course Content

Type: Optional– PEC&AC Track – 3rd Trimester

Module A. Introduction. The Homogeneous Universe
The standard Cosmological Model. Cosmological parameters.
Problems of the Big Bang model.
The Inflationary solution.

Module B: The Non-Homogeneous Universe: Perturbations in the Matter Distribution
Linear theory of perturbation evolution in Friedmann universes.
Non-linear perturbation theory: Zeldovich approximation and N-body simulations.

Module C: Background Radiation
Propagation of a radiation field in an inhomogeneous Friedmann Universe.
Origin of anisotropies in the Background Radiation: Sachs-Wolfe effect, integrated Sachs-Wolfe effect.
Acoustic oscillations on the last scattering surface. Adiabatic and isocurvature modes.
Recent observations and implications for structure formation models. Cosmological parameters.
Sunyaev-Zeldovich effect: hot gas in clusters and secondary anisotropies in the background radiation.

Module D: Large-Scale Structure
Observations of matter distribution.
Statistical methods in Cosmology.
Measurement of the correlation function and power spectrum from galaxy catalogs.
Luminosity functions and mass functions. Comparison between simulations and observations.
Baryon acoustic oscillations in the galaxy distribution. Spectroscopic and photometric surveys.
Determination of cosmological parameters from large-scale structure.

Module E: Gravitational Lenses
History. Basic concepts.
Equations of gravitational lensing effect.
Strong and weak lenses.
Applications in Cosmology.

Reading List

• Modern Cosmology – S. Dodelson. Academic Press (2003).
  The Cosmic Microwave Background – R. Durrer. Cambridge University Press (2008).
• The Early Universe – E.W. Kolb, M.S. Turner. Addison-Wesley (1990).
• The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure – D.H. Lyth, A. Liddle. Cambridge U.P. (2009).
• Statistics of the Galaxy Distribution – V. J. Martínez and E. Saar. Chapman & Hall (2002).
• Structure Formation in the Universe – T. Padmanabhan. Cambridge U. P. (1993).
• Cosmological Physics – J.A. Peacock. Cambridge University Press (1998).
• Large Scale Structure of the Universe – P.J.E. Peebles. Princeton U.P. (1980).
• Cosmology – S. Weinberg. Oxford U.P. (2008).
• Extragalactic Astronomy and Cosmology – P. Schneider. Springer-Verlag (2006).
• Dark Energy – Yun Wang. Wiley-VCH (2010).
• Practical Statistics for Astronomers – J.V. Wall and C.R. Jenkins. Cambridge Univ. Press.
• Measuring our Universe from Galaxy Redshift Surveys, O. Lahav and Y. Suto (2004)
• Lectures on Gravitational Lensing, Ramesh Narayan & Matthias Bartelmann (1996), astro-ph/9606001
• Gravitational Lensing in Astronomy, Joachim Wambsganss (1998), Living Reviews,
• Cosmological Parameters from Observations of Galaxy Clusters, S. Allen (2011)
• The evolution of the large-scale structure of the universe: beyond the linear regime, F. Bernardeau (2013)
• Dark Energy and CMB (S. Dodelson et al., 2013)
• Distance Probes of Dark Energy (Kim, Padmanabhan et al., 2013)
• Cosmological Perturbation theory (classic paper by Ma and Bertschinger)
• Planck cosmological results
• Supernova Ia cosmology
• Dark energy review

All the course information is available on its website.

Teaching Plan Information

Course Schedule

Academic Team

Course Content

Type: Optional– PEC&AC Track – 3rd Trimester

This course has been taught in the postgraduate programmes at Madrid Autónoma University, Durham University, the University of Valencia (2018), and The Max Planck Institute München (2009). It has also been taught (in different formats) in a number of postgraduate schools: Taller de Altas Energías (TAE 2014, 2015, 2017, 2018, 2019, 2021), 1st International School on Particle Physics and Cosmology (UIMP 2019), Higgs Centre School of Theoretical Physics (2016), STFC HEP School (2015, 2016, 2017).

Some notes for the course (pdf).
Exercises (pdf).
Extra exercise (pdf).

1.- Introduction

In this session, we present the observational evidence that points towards the existence of dark matter. We introduce the concept of dark matter halo and think about its properties (slides).

2.- Cosmology 101

A brief reminder of Early Universe Cosmology. Emphasis is put on how to compute the abundance of a given species in equilibrium. The Boltzmann equation that describes the evolution of the number density is derived (slides).

3.- Dark Matter Production (Freeze-out)

We apply the Boltzmann equation to the case of a non-relativistic DM particle that “freezes-out”, and define WIMPs (slides).

4.- Dark Matter Production (WIMP models and Freeze-in)

We study some specific particle realisations of WIMPs (concentrating on simplified models) and study special cases, such as resonant annihilation and co-annihilations. We then introduce a new paradigm, where dark matter with very small couplings “freezes-in” (slides).

5- Axions

We review the misalignment mechanism for the production of axions. The cosmological implications are reviewed. We then comment on axion detection.

6- Direct Detection

We show the basics of direct dark matter detection. We derive the equation for the observed detection rate and comment on uncertainties associated to nuclear physics and astrophysical parameters of the dark matter halo (slides).

EXERCISES

Exercises for the course (solutions available upon request) (pdf). 

Extra exercise (pdf)

Reading List

Group Theory:
1) H. Georgi: “Lie Algebras in Particle Physics”,
2) H.F. Jones: “Groups, Representations and Physics”
3) J.F. Cornwell: “Group Theory in Physcis”, Vols. 1,2

Differential Geometry:
1) Nash, Sen: “Topology and Geometry for Physicists”
2) M. Nakahara: “Geometry, Topology and Physics”

All the course information is available on its website.

Teaching Plan Information

Course Schedule

Academic Team

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

Teaching Plan Information

Course Schedule

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