Physics, Second Cycle
1. in 2. year
Hours per week – 2. semester:

Enrollment into the program. It is advised to be familiar with basics of the theories of gravitation and of elementary particles.

Content (Syllabus outline)

Homogeneous cosmological model: Hubble diagram, coordinate systems, Newton cosmology, General theory of relativity, Friedman-Robertson-Walker metrics, Friedman-Lemaitre equations. Cosmic inventory: photons, barions, dark matter, neutrinos (ultrarelativistic matter), dark energy. Boltzman equation, nucleosynthesis, recombination and occurrence of background radiation. Measurements of the Hubble constant and history of expansion of the Universe. Barionic acoustic oscillations.
Perturbations in the Universe in linear theory: Scalar, vector and tensor perturbations. Perturbations in dark matter: evolution before and after the period of matter-energy equality, entrance into horizon, transfer functions and power spectra. Measurement of galaxy distribution, weak lensing and Lyman-alpha forest. Cosmological limits to neutrino mass. Perturbations in plasma before decoupling; power spectrum of anisotropies in background radiation: large scales, acoustic modes, small scales; measurements of anisotropies in the background radiation.
Early universe and inflation: Problem of boundary values. Sakharov conditions. Motivation for inflation, its implementation with a scalar field, formation of tensor and scalar perturbations. Approximation of slow roll solution, spectral indices, observational methods to limit inflation parameter values.


• Scott Dodelson: Modern Cosmology, Academic Press 2003,
• Andrew Liddle: An Introduction to Modern Cosmology, John Wiley 2003,
• Viatcheslav Mukhanov: Physical Foundations of Cosmology, Cambridge University Press, 2005,
• Thanu Padmanabhan: Cosmology and Astrophysics through problems, Cambridge University Press 1996,
• Lars Bergström, Ariel Goobar: Cosmology and Particle Astrophysics, Springer 2006,
• Houjun Mo, Frank van den Bosch, Simon White: Galaxy Formation and Evolution, Cambridge University Press, 2010.

Objectives and competences


The main objective is to gain understanding of the standard cosmological model. Special emphasis is given to basic assumptions (homogeneity, isotropy, the universe looks the same whoever and wherever you are) and their observational confirmation.


Students learn statistics as a fundamental tool to constrain both cosmological and fundamental physics.

Intended learning outcomes

Knowledge and understanding:
Basic understanding of the standard theory of the formation and evolution of the Universe and of measurements that support this theory. Cosmology as a tool to constrain fundamental theories.

The acquired knowledge is the basis for studying theoretical and observational cosmology at the graduate level.

The course offers examples of usage of principles of symmetry and statistics, understanding of assumptions in interpretation of cosmological data.

Transferable skills:
Advanced understanding of statistics of random normally-distributed fields, a specific example of perturbation theory in general theory of relativity.

Learning and teaching methods

Lectures, numerical exercises, homework, consultations, review of the literature.


Final written exam or exams from exercises during the course
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

doc. dr. A. Slosar:
1. Slosar, A., et al. 2013, Journal of Cosmology and Astroparticle Physics, Issue 04, article
id. 026, Measurement of baryon acoustic oscillations in the Lyman-alpha forest fluctuations
in BOSS data release 9
2. Lombriser, L., Slosar, A., Seljak, U., Hu Wayne, 2012, Physical Review D, vol. 85, Issue
12, id. 124038, Constraints on f(R) gravity from probing the large-scale structure
3. Slosar, A., et al. 2011, Journal of Cosmology and Astroparticle Physics, Issue 09, id. 001,
The Lyman-alpha forest in three dimensions: measurements of large scale flux correlations
from BOSS 1st-year data
4. Slosar, A. 2009, Journal of Cosmology and Astroparticle Physics, Issue 03, id. 004,
Optimal weighting in fNL constraints from large scale structure in an idealised case
5. Slosar, A., et al. 2008, Journal of Cosmology and Astroparticle Physics, Issue 08, id. 031,
Constraints on local primordial non-Gaussianity from large scale structure