NFYK16010U Particle Physics and the Early Universe

Volume 2022/2023

M.Sc. programme in Physics


The aim of the course is to familiarize students with modern theories of particle physics and cosmology, the theory of inflation, the theory of dark matter and dark energy in combination with the physics of cosmological gravitational waves and black holes. Specifically, in addition to modern theoretical approaches, students will gain hands-on experience in analyzing data from space (WMAP, Planck experiments), particle accelerator data, and even the recently released LIGO data. This course is central to any subsequent courses or projects that require an understanding of modern particle physics and cosmology.

The lectures study the basic principles of modern field theory in relation to the fundamental problems of modern cosmology.

Approximately 30% of the lecture time and practical exercises are devoted to the study of the Big Bang theory, including the theory of gravitational instability, which leads to the formation of structures in the Universe. We will focus on the role of dark matter as a basis for the formation of structures in the Universe and emphasize the role of dark energy as a source of inflation in the modern Universe. The main task of this block is to familiarize and analyze the problems of physical cosmology, the solution of which is impossible without invoking the ideas of the theory of inflation.

The remaining 70% of the lectures explain how the principles of modern field theory are used in inflation theory to explain the fundamental properties of space and time. Using the prediction of the Standard Particle Model, students will become familiar with emerging Higgs-based inflation regimes and explore general approaches to constructing inflaton potential. The main task of this block is to study the physical consequences of inflation, which are manifested in the heating of the cosmic plasma (Big Bang) and the formation of primary inhomogeneities, which are the embryos of structures in the modern Universe.

Throughout the course we will use the CMB data to understand the observational status of inflation.

Learning Outcome


To achieve the goals of the course and exam the students should know:

  • Basic principles of the Bing Bang theory and Standard Particle Model.
  • Classification of epochs of the cosmological expansion.
  • Cosmological solutions for scalar factor for different equations of state of the matter, provided by the Standard model.
  • Motivation for Inflation. Basic equation of evolution of the vacuum state of the matter in the Universe.
  • Solution of fundamental problems of the cosmology in the theory of inflation ( initial conditions of inflation, particle horizon, origin of the primordial perturbations, creation of matter due to decay of
  • inflaton)
  • Origin of the Cosmic Microwave Background (CMB). Testing the theory of inflation by the modern CMB experiments (the WMAP and the PLANCK) .
  • Possible explanation of the origin of the Dark Matter and the Dark Energy and corresponding uncertainties.


The student will after the course know the basic theories of the modern cosmology and high energy physics, and will have an experience in the gravitational waves physics.

Students will gain a basic knowledge of modern physical cosmology, including inflation both in the early stages of the evolution of the Universe and at the present days (Dark Energy).

Students will gain skills in constructing multi-parameter models and analysis of their asymptotic behavior. Students will gain work experience with the observational data of the Planck experiment and their use to determine the parameters of the Standard Cosmological Model and the theory of inflation.

See Absalon for final course material including Notes. The following is an example of expected course literature.

V.Mukhanov, Physical foundation of cosmology. Cambridge University Press. 2005 Ian Moos:” Quantum theory, black holes and inflation”, John Wiley and Sons Ltd.

P.Naselsky, D. Novikov and I. Novikov,” The physics of the Cosmic Microwave Background”, Cambridge University Press.2006

General skills in math and computation, atomic and nuclear physic are required according to the M.Sc. program in Physics.
An advanced courses on quantum mechanics and particle physics are recommended for basic knowledge.
Academic qualifications equivalent to a BSc degree is recommended.
Lectures and exercises
  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 132
  • Practical exercises
  • 24
  • Exam
  • 8
  • Total
  • 206
7,5 ECTS
Type of assessment
Continuous assessment
Written assignment, 3 hours
Type of assessment details
Homework during the course counts towards 20% of the final grade.
Written homework during the exam week counts for the remaining 80%.
The exam questions are based on the list of topics provided in the Course Notes Table of Contents.
In the written assignment for the exam, three theoretical questions will be taken from the Table of Contents and three questions will be presented in the form of problems.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
More internal examiners

same as ordinary exam

Criteria for exam assesment

In order to obtain the grade 12 the student should convincingly and accurately demonstrate the knowledge, skills and competences described under learning outcome.