Cosmology (MKTP5)

Lecturer:
Prof. Dr. Matteo Maturi (ITA/ZAH, ITP)
Head tutor: Francesco Gozzini (gozzini@thphys.uni-heidelberg.de)

Space and time:

• Winter semester, 2025/26
• From October 16th to January 30th
• Thursday 14:15-16:00 (INF308/HS 2)
• Friday 14:15-16:00 (INF308/HS 2)

Overview:
The lectures will introduce the foundations of modern cosmology. Topics include the basics of General Relativity, the modeling of a homogeneous and isotropic universe, dark matter, the cosmological constant and dark energy, cosmic inflation, and the thermal history of the universe, including cosmological nucleosynthesis and the cosmic microwave background. We will also study cosmic structure formation in both the linear and non-linear regimes. After establishing the theoretical framework, the course will explore the key observational evidence that underpins our current understanding of the universe.

Objectives

• Gain a broad overview of modern cosmology and its fundamental concepts.
• Understand the theoretical framework used to describe the universe, from General Relativity to cosmic structure formation.
• Learn how dark matter, dark energy, and cosmic inflation fit into our cosmological models.
• Become familiar with the thermal history of the universe and its key processes.
• Appreciate the connection between theory and observations, and how experimental data shapes our current picture of the cosmos.

Prerequisites:
PTP2 and General Relativity are helpful but not mandatory.

Format:
The lectures will be held in person and will be recorded. Lecture notes about what will be present at the blackboard and additional material will be provided. The notes will be complementary to other material/books and present full derivations. I will start slow to build a solid background. The lectures and exercise classes are held in English.

Enrollment:
To get credit points for the lectures it is necessary to enroll through heiCO. If you are still missing the credentials (immatriculation, ID number, ...) and can not log-in, ask the head tutor to be enrolled manually.

Material and exercises:
You find everything in this page.

Exam:
February 12th 2026, 9am, room gHS in Philosophenweg 12
The revision of the exam will take place on Monday 16th 

Exam review:
TBD. Two or three days after the exam.

Admission to the exam:
Attend at least 70% of the tutorials AND gain 5 points in different tutorials by: Presenting an exercise (1 point) or actively participating in the discussion during the tutorials (max 1 point). If participation is below 70%, it is required to hand in 3 full exercise sheets (before their discussion during the tutorials) that will be graded.

Lehre, Studium und Forschung:
Lecture Token MKTP5 (8CP): heiCO
 

Index of the lectures

Introduction
    - What is cosmology about?
    - History of cosmology at large
    - Special relativity
    - General relativity

Homogeneous and isotropic universe
    - Einstein equations
    - Friedman-Lamaitre-Robertson-Walker (FLRW) metric
    - Friedmann equations   =>  H(a), ρ(a), T(a)
    - The cosmological parameters
    - The ingredients: radiations, dark matter, baryons, dark energy/lambda
    - Distances in cosmology
    - The distance ladder

Dark energy
    - The cosmological constant lambda
    - Problems of lambda
    - Dark energy model
    - Equation of state of dark energy
    - Modifying gravity, example: Horndeski theory

Dark matter
    - Properties
    - Particle candidates
    - Indirect detections
    - Direct detections
    - Problems

Cosmic inflation
    - Solving problems of the Hot Big-Bang model
    - The inflaton field
    - Origin of the initial energy density fluctuations
    - Constraints on inflation

Thermal History
    - Summary of equilibrium thermodynamics
    - Cosmological nucleosynthesis
    - Neutrino decoupling (CνB)
    - Matter-radiation decoupling (CMB)

Linear structure formation
    - Origin of the fluctuations
    - Hydrodynamics (Continuity, Euler, Poisson)
    - Linearization, perturbative approach
    - Set comoving coordinates
    - The growth factor D+(a)
    - Relativistic structure formation
    
Statistics of the perturbations
    - The power spectrum and the correlation function
    - Normalization of the power spectrum and σ8
    - CDM power spectrum
    - The bias factor
    - Peculiar velocities
    - BAOs
    - Non linear correlations

Non linear structures
    - The Zel’dovich approximation
    - Spherical collapse
    - Press-Schechter mass function
    - N-Body numerical simulations
    - Other mass functions
    - Dark matter haloes: profiles, virial theorem
    - Galaxies: types, velocity profiles
    - Clusters of galaxies: X-rays, SZ, Optical, baryonic fraction, mass estimates

Observations and cosmological probes
    - CMB
    - Type-Ia supernovae
    - Galaxy clustering
    - Redshift-space distortion
    - Gravitational lensing
    - Galaxy clusters

Videos of the lectures
    - Videos will be posted two weeks after the corresponding lecture: Link

Suggested talks sereis:
   - Heidelberg Joint Astronomical Colloquium (HJAC)

Suggested readings:
    - the scripts you find below in the "Material" section
    - the following books you find in the university library:
      Cosmological Physics (John A. Peacock)
      Modern Cosmology (S. Dodelson, F. Schmidt)