<< Cosmo

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Course ID:

• 0800-WZAT-3

Semester/year:

• summer 2025/2026

Erasmus code:

• 13.7

Course title:

• Cosmic topology Name in Polish: Topologia kosmiczna

Department:

• 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:

• http://cosmo.astro.uni.torun.pl/foswiki/bin/view/Cosmo/MonographCosmoOpisShapeUniverse

ECTS credit allocation (and other scores):

• 2.00 (some years this may be 3.00 OR 5.00; differs over time)

Number of contact hours:

• 20

Language:

• 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 observational methods of measuring cosmic topology and briefly covering the theory of topological acceleration

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 background

• topological acceleration

• beyond the FLRW model: the Earth exists

Bibliography:

• 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

Prerequisites:

required:

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

recommended:

• 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 for the three signs of curvature

* social skills: experience in subjecting one's learning to potentially intensive peer review

* see also 0800-M-SHAUNI K_W, K_U, K_K codes

Assessment criteria:

* Form of the exam: to be negotiated.

Practical placement:

• Initial steps towards observational cosmology research.

-- BoudRoukema - 12 Dec 2025