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MAS347 MATHEMATICAL ASPECTS OF COSMOLOGY

Recommended books:

Rowan-Robinson, Cosmology (3rd Edition)
J. Silk, The Big Bang (Freeman 2nd Edition)
M. Berry, Principles of Cosmology and Gravitation.
J. Islam, An Introduction to Mathematical Cosmology
B. J. Carr, Cosmology - old lecture notes.

KEY OBJECTIVES:

Course-work 10%, exam 90%

1. Cosmography of Universe:
You should have a good qualitative understanding of the contents of the Universe and its key observational features: galaxies, large-scale structure, matter and radiation content, cosmological principle, cosmic expansion and Hubble law.

2. Cosmic Microwave-background radiation (CMB):
You should understand what information about the structure and evolution of the Universe can be obtained from the spectrum and small anisotropy of the CMB.

3. Newtonian Cosmological models:
You should be able to derive the acceleration and Friedmann equations for the evolution of the scale factor and solve them within framework of Newtonian theory.

4. Relativistic Cosmological models:
You should be able to work with the equivalent relativistic equations (the deceleration and Friedmann equations, equation of state and the energy conservation equation), using them for determination of the scale factor as a function of time and for obtaining key relationships between fundamental cosmological parameters at the present moment (Hubble constant, Ho, dimensionless density, Omegao, deceleration parameter, qo, and the Lambda-term).

5. Brief History of Universe:
You should be able to derive the age of the Universe in the models with Lambda = 0. You should understand the dynamical role of matter, radiation, dark energy and curvature in the evolution of the scale factor; you should have a general idea of processes at the epoch of recombination and be able to explain why and when the decoupling of matter and radiation takes place; you should also understand why the formation of the large scale structure in the Universe can start only after recombination.

6. Inflation:
You should understand the basic ideas of inflationary models and understand under what conditions the expansion of the Universe runs with acceleration.

7. Mathematics of Observational Cosmology:
You should understand how to use the Robertson-Walker metric to study the propagation of light-rays and to calculate distances, surface areas and volumes; you should understand the significance of the particle horizon and cosmological redshift; you should be familiar with the various distance measures (angular diameter and luminosity distances) and their application in cosmological tests.

8. Origin of Large scale structure:
You should be familiar with the mechanism of gravitational instability; you should be able to derive and solve the evolution equation for small density perturbations in the simplest (p = 0, Lambda  = 0) cosmological model.

MAS347 Mathematical Aspects of Cosmology - 2008 Lecture notes 21-25:

  • 2008 sample exam

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