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Cosmology and Structure Formation

Module PH2248

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2022/3 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3WS 2021/2WS 2020/1WS 2019/20SS 2018SS 2017

Basic Information

PH2248 is a semester module in German or English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2248 is Mathias Garny.

Content, Learning Outcome and Preconditions


Foundations of modern cosmology: Friedmann-Robertson-Walker metric, Friedmann equations, expansion, early Universe, perturbative expansion around the homogeneous solution, cosmic microwave background radiation (CMB), acoustic oscillations, structure formation, power spectrum, impact of cosmic neutrino background and neutrino mass, origin of density perturbations and inflation

Learning Outcome

After successful completion of the module the students are able to:

  • understand current questions of cosmology
  • solve the Friedmann equation
  • know the influence of Dark Matter, Dark Energy, and Neutrinos on anisotropies in the cosmic background radiation and structure formation
  • to use theoretical tools to calculate the dynamics of the baryon photon Plasma in the early universe
  • to calculate density fluctuations in different epochs (material dominated, radiation dominated) and on different scales.
  • understand and apply theoretical descriptions (linearized Einstein equations, Boltzmann equations, Compton scattering)
  • understand the processes that determine the observed temperature fluctuations in the cosmic background radiation (Sachs-Wolfe effect, Doppler, Integrated SW Effect)
  • know indications of inflationary expansion in the early universe, theoretical description of scalar field models and the origin of th density fluctuations
  • make quantitative predictions of inflation and to compere them with observations


    No preconditions in addition to the requirements for the Master’s program in Physics. Knowledge of general relativity is helpful, but not compulsory.

    Courses, Learning and Teaching Methods and Literature

    Courses and Schedule

    VO 4 Cosmology and Structure Formation Garny, M. Tue, 16:00–18:00, PH 3343
    Thu, 12:00–14:00, PH 3344
    UE 2 Exercise to Cosmology and Structure Formation Garny, M. dates in groups

    Learning and Teaching Methods

    The module consists of a lecture and an exercise class.

    Starting from general physical principles (equations of motion derived from variation of an action, thermoynamics, Boltzmann-Equations) the physical processes that are relevant for cosmology will be discussed systematically in a comprehensible way in th electure. Also  examples, overview over modern questions and methods are given. The lecture is given mainly on blackboard.

    In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.


    Presentation, blackboard, problem sheets


    • S. Dodelson: Modern Cosmology, Academic Press, (2003)
    • S. Weinberg: Gravitation and Cosmology, John Wiley & Sons, (1972)
    • E.W. Kolb & M.S. Turner: The Early Universe, Westview Press, (1994)
    • J. Lesgourgues & S. Pastor: Neutrino cosmology, Cambridge University Press, (2013)

    Module Exam

    Description of exams and course work

    There will be a written exam of 60 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

    For example an assignment in the exam might be:

    • Explanation of physical processes relevant for structure formation and the cosmic microwave background
    • Impact of dark matter, dark energy, neutrinos on structure formation
    • Impact of various cosmic parameters on the cosmic microwave background
    • Evolution of density perturbations in various epochs, relevant scales and processes, theoretical description
    • Hints for inflation, predictions, theoretical description
    • Linearized Einstein and Boltzmann Equations, relevant processes, approximations
    • reionization

    Exam Repetition

    The exam may be repeated at the end of the semester.

    Current exam dates

    Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

    Exam to Cosmology and Structure Formation
    Mon, 2024-02-05 till 23:55 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin vor 23.03.2024. // Dummy date. Contact examiner for individual appointment. Registration for exam date before 2024-Mar-23. till 2024-01-15 (cancelation of registration till 2024-02-04)
    Mon, 2024-03-25 till 23:55 Dummy-Termin. Wenden Sie sich zur individuellen Terminvereinbarung an die/den Prüfer(in). Anmeldung für Prüfungstermin zwischen 25.03.2024 und 20.04.2024. // Dummy date. Contact examiner for individual appointment. Registration for exam date between 2024-Mar-25 and 2024-Apr-20. till 2024-03-24
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