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Course ID:

  • 0800-M-SOU1-DY


  • summer 2012/2013

Erasmus code:

  • 13.7

Course title:

  • The Shape of the Universe part I Name in Polish: The Shape of the Universe part I


  • Faculty of Physics, Astronomy and Informatics

Course groups:

(in Polish) Astronomia s2. Wykłady monograficzne do wyboru (in Polish) Fizyka s2. Wykłady monograficzne do wyboru (in Polish) Wykłady monograficzne do wyboru (wszystkie oferowane w danym roku akademickim)

Course homepage:

ECTS credit allocation (and other scores):

  • 3.00 OR 5.00 (differs over time)

Number of contact hours:

  • 30


  • English

Brief description:

  • Formal and intuitive introduction to the comoving spatial section of the Universe according to the Friedmann-Lemaitre-Robertson-Walker model, i.e. as a constant curvature 3-manifold, primarily focussing on empirical measurements of the two main properties of space: curvature and topology.

Full description:

  • space as a 3-manifold: curvature + topology

  • curvature and the metric, the role of the Einstein-Hilbert equations in hot big bang cosmology

  • comoving coordinates, scale factor, local cosmological parameters, Friedman equation, fluid equation, acceleration equation

  • multiply connected 3-manifold, fundamental domain, apparent space

  • 3-dimensional empirical approaches

  • 2-dimensional empirical approaches: identified circles principle, cosmic microwave backround

  • ongoing research project

  • beyond the FLRW model: the Earth exists


  • Liddle, A.R., 2000, Introduction to modern cosmology, 2nd edition if possible

  • Roukema, B.F., 2000, The Topology of the Universe, Bull.Astron.Soc.India 28 (2000) 483, arXiv:astro-ph/0010185

  • Peebles, P.J.E., 1993, Principles of physical cosmology, Princeton: Princeton University Press



  • elementary algebra; calculus; three-dimensional Euclidean geometry; Newtonian physics;


  • basic astronomy; spherical astronomy; extragalactic observational astronomy; differential geometry; special and general relativity

Learning outcomes:

* knowledge: geometrical, topological, physical, algebraic and numerical familiarity with the present state of empirical knowledge about the whole of the observable Universe and common definitions of the size of the Universe

* knowledge: awareness of the role of open access to scientific empirical data and theoretical tools and FLOSS software for scientific analysis in modern scientific research (FLOSS: free/libre/open source software)

* skills: the ability to make elementary geometrical calculations for the main cosmological distance definitions (4 points in exam) for the three signs of curvature

* social skills: experience in subjecting one's learning to potentially intensive peer review (1 point in exam)

Assessment criteria:

* The exam consists of four points from html/latex/WIMS exercises which test the student using questions randomly chosen from an N-dimenionsal parameter space of questions where N varies from about 8 to 18, and one creative point offering the student the chance to subject his/her learning to potentially intensive peer review.

Practical placement:

  • Initial steps towards observational cosmology research.
Topic revision: r1 - 20 Apr 2012, BoudRoukema
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