2017/18 Undergraduate Module Catalogue

MATH3531 Cosmology

10 creditsClass Size: 110

Module manager: Professor Serguei Komissarov
Email: S.S.Komissarov@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2017/18

Pre-requisite qualifications

MATH1012 or MATH1400 or PHYS1200, or equivalent.

This module is approved as a discovery module

Module summary

This module introduces students to the basic mathematics and physics of modern Cosmology. The main focus is on the geometry of the Universe and theoretical models of its evolution, which can be addressed without relying of solid foundations in physics and astronomy.

Objectives

To introduce the student to the mathematics and physics of the large scale structure and motion of the universe.

On completion of this module, students should be able to:
a) state the main connections between the theories of classical mechanics, special and general relativity, and quantum mechanics;
b) explain the main observational features of galactic motion using the ideas of measurement of distance, parallax, Doppler shift and luminosity;
c) calculate particle motion in the framework of Newtonian gravitation;
d) demonstrate the relation between Hubble's law and the Cosmological Principle;
e) derive the differential equation for the cosmological scale factor and produce solutions in special cases.

Syllabus

The topics covered include:

1) Outline of the current astronomical results on structures and composition of the Universe, the cosmological redshift, and the Hubble law;
2) Euclidean space, its metric form, lengths, areas and volumes. Geometry of Euclidean sphere; Non-Euclidean geometries.
3) Space, time, and gravity in Newtonian physics, Special Relativity, and General Relativity - an outline of key ideas and basic results. The concept of spacetime and its curvature. 3+1 representation of spacetime metric.
4) The Walker-Robertson metric of uniform Universe and Friedmann's equations.
5) Expansion of the Universe. The Hubble constant and the deceleration parameter. The critical density.
6) Friedmann's models of open, flat and closed universes. The Big Bang theory. The cosmic microwave background radiation.
7) Distances to sources with given redshift. The angular size and luminosity ``distances''. The cosmological horizon.
8) The Cosmological constant and supernovae projects. The accelerating expansion of the Universe. Dark matter and dark energy.
10) The flatness and horizon problems of Friedmann's cosmology. Basic ideas of the inflation model.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	27	1.00	27.00
Private study hours			73.00
Total Contact hours			27.00
Total hours (100hr per 10 credits)			100.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 26/04/2017

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