Syllabus
Introduction -- beginnings of cosmology and its definition; naive models and their representatives (Bruno, Galilei, Newton, Halley, de Chéseaux and others); concept of homogeneity and isotropy; statistical tests; distances and time-scales in the Universe; Olbers paradoxon; inhomogeneity in the distribution of stars; structure and dimensions of our Galaxy; distance of galaxy M31 in Andromeda; redshifts and the Hubble relation; distribution of extragalactic objects.
Overview of the theory of symmetric manifolds -- Killing vectors; scalars, vectors and tensors in maximally symmetric manifolds; Ricci tensor; Ricci scalar; Minkowski, de Sitter and anti-de Sitter metrics; maximally symmetric submanifolds; Friedmann metric and its derivation.
Maximally symmetric manifolds in cosmology -- perfect cosmological principle; steady-state Universe.
Cosmography -- cosmological principle; Friedmann-Robertson-Walker metric; comoving coordinates; conformal time; redshift; definition of cosmological distances; Pogson relation in cosmology; relation between distance and redshift; K-correction.
Standard cosmological model and its equations -- Einstein equations without pressure and with pressure; critical density; Friedmann equation and its solutions; cosmological constant; Einstein model; omega-factors; deceleration parameter; horizon.
Observational tests of the standard cosmological model -- cosmological tests of homogeneity and isotropy; mean density of matter and radiation; dark and radiating matter; helium and other elements abundance in the Universe; accelerating Universe; cosmic microwave background radiation.
Annotation
First semester of a course of cosmology. Introduction; overview of the theory of symmetric manifolds; maximally symmetric manifolds in cosmology; cosmography; standard cosmological model and its equations; observational tests of the standard cosmological model. Intended primarily for master and PhD students of astronomy and astrophysics, theoretical physics and particle and nuclear physics. Knowledge of the general theory of relativity at the level of NTMF111 (General theory of relativity) course is assumed.
Emphasis is put on the cosmological aspects of the astronomical observations.