Introduction
You have two weeks to complete this unit. Below I give a syllabus for the unit, together with guidance as to where you can find the relevant material. More detailed advice on how to approach the work is given in the introduction to Unit 1, and will not be repeated here.
This unit contains the theoretical core of the course, and the conceptual challenges which go with it. You should be prepared to spend about 15 hours on the unit, plus a further 4 hours for the assessed exercise.
Syllabus and source
This unit covers the core theory needed to understand modern developments in observational cosmology. A full G.R. treatment would start from the Robertson-Walker metric, which is inserted into Einstein's field equations to derive the Friedmann and acceleration equations. This is unnecessarily complex for our purposes, since the dynamical equations can be derived and understood from a Newtonian perspective, and this is the route we will take. A course note on the subject is available below. The lecture for this module will also be used to discuss solutions to these equations, and the nature of the cosmological constant.
Despite this Newtonian approach, familiarity with the R-W metric and
spatial curvature are essential to interpreting cosmological
observations, so these will also be introduced.
Topic | Sources | Comments |
Dynamical equations of the Universe: Assumptions - Newtonian treatment The Friedmann equation The acceleration equation |
RR(4.3, 5.1), L1,L2,L3(3.0-3.6) | |
Solutions to the equations with Lambda=0: For matter (dust); radiation; matter + radiation Flat, open and closed Universes Behaviour of the scale factor with time |
L1(4), RR(4.6) L2,L3(5) |
|
Cosmological Parameters : H,q,Omega,Lambda - meanings and definitions |
L1,L2,L3(6), RR(4.7) | |
The cosmological constant: Friedmann equation with Lambda term Physical interpretation Dynamical solutions - static & accelerating Universes |
L2,L3(7), L1(6.4), RR(4.8) |
|
Curved space-time Flat, spherical and hyperbolic geometries Relation to the Friedmann models |
L1(5), L2,L3(4), RR(4.4, 4.5) |
|
The Robertson-Walker metric The form and meaning of the R-W metric General Relativity also gives the Friedmann equation |
RR(4.4, 4.5), L2,L3(A1.1) |
|
Cosmological Redshift Relation between redshift and expansion (& scale factor) |
L1(4.2), RR(7.4) L2,L3(5.2, A2.1) |
|
Age of the Universe Dependence on Ho, and Omega (for Lambda=0) Comparison with ages of stars Effect of the cosmological constant |
L1(7), RR(4.9 & p.163) L2,L3(8) |
Notes
- Key: RR=Rowan-Robinson (4th edition), L1=Liddle (1st edition) - relevant sections, or sometimes complete chapters, eg L(5), are given in brackets. L2=Liddle, 2nd edition, L3=Liddle, 3rd edition,. Older editions of Rowan-Robinson give an out-of-date treatment of the cosmological constant.
- The topics listed are not of equal size.
- References given are not by any means the only ones (e.g. check out some of the suggested reading material and other references) but they should provide a reasonable treatment.
- For the more complex topics (such as the distance scale) it pays to consult several sources and to synthesise the results. This takes longer, but should result in a better understanding.
Unit 2: Cosmological theory
Introduction
Syllabus and sources
Self-test problems
Units
- The Hot Big Bang
- Cosmological theory
- Evolution from the Big Bang
- Dark matter & baryons
- Observational properties and cosmological tests
Contact
Email:
Office: Physics West, 223