ASTM108 Cosmology/MTH703U Advanced Cosmology


Course information

Lecturer

Prof. J. E. Lidsey
e-mail: J.E.Lidsey@qmul.ac.uk
Office: Room 455, School of Mathematical Sciences

Lectures

There are two weekly lectures: Tuesday 14.00-16.00 (both in the Maths Building, Room 103).

NB LECTURES START ON TUESDAY 28 SEPTEMBER

Mobile phones must be switched OFF in lectures.

Office Hours, Room 455, Mathematical Sciences

Tuesday 16.30 - 17.30

Wednesday 11.30 - 12.30

NB THERE IS NO READING WEEK FOR THIS COURSE. LECTURES ON TUEDAY 9 NOVEMBER AS NORMAL



Course Profile

Welcome to ASTM108 Cosmology. Cosmology is a rapidly developing subject that is the focus of a considerable research effort. It is the attempt to understand the present state of the universe as a whole and thereby shed light on its origin and ultimate fate. Why is the universe structured today in the way that it is, how did it develop into its current form and what will happen to it in the future? The aim of this course is to address these and related questions from both the observational and theoretical perspectives. The course does not require specialist astronomical knowledge and does not assume any prior understanding of general relativity.

I hope you enjoy the course and wish you all well. Let's enjoy it together which for me means plenty of feedback from you during the term. This can be through questions in class, during the office hour or by email. Please ask questions - it's much more fun having some feedback!

Objectives

By the end of the course you should be able to:

1. Identify the main evidence for an expanding universe.

2. Derive and solve the equations determining the cosmic expansion in a number of different settings and use the Friedmann equation.

3. Explain the relationship between different cosmological models and observable parameters.

4. Calculate the age of the universe.

5. Describe possible outcomes for the future destiny of the universe.

6. Summarize the evidence for, and explain the effects of, a cosmological constant.

7. Explain the physics of the early universe and describe the observational evidence for the big bang.

8. Identify and explain the problems of the big bang model and describe how these are solved by inflation.

9. Discuss the evidence for dark matter in the universe.

10. Explain the physics that leads leads to structure formation.

11. Explain the physics behind the cosmic microwave background and explain the origin and consequences of the fluctuations in its temperature.

Syllabus

Observational Overview: structure of the visible universe; redshift and Hubble's law; the cosmic microwave background radiation; Cosmological Principle; relation between Cosmological Principle and Hubble's law.

Newtonian Cosmology and the Cosmological Equations: Friedmann equation; conservation equation; equation of state; acceleration equation.

Solving Friedmann's Equation: expansion of a pressureless universe; expansion of a universe dominated by radiation; relationship with redshift.

Density and Destiny of the Universe: Distance in the universe; deceleration parameter; Omega-parameter; relationship between density and fate of the universe.

The Age of the Universe: Calculating the cosmic age; dependence on Hubble parameter and Omega-parameter; the age problem.

The End of the Universe: collapse of a universe dominated by radiation; collapse of a pressureless universe.

The Cosmological Constant: interpretation of the cosmological constant; observational evidence for a cosmological constant; age of the universe with a cosmological constant; fate of the universe with a cosmological constant.

The Early Universe: density of radiation today; particles in the early universe; the ratio of photons to baryons; origin of the cosmic microwave background; relativistic and non-relativistic particles; relationships between temperature and age of the universe.

Primordial Nucleosynthesis: equilibrium processes; neutron freeze out; deuterium bottleneck; production of light elements; comparison with observations.

Problems with the Big Bang Model: flatness problem; horizon problem; monopole problem.

Inflationary Cosmology: definition of inflation; solution to the flatness problem; solution to the horizon problem; solution to the monopole problem; predicted value of Omega.

Dark Matter: evidence for baryonic dark matter; evidence for non-baryonic dark matter; dark matter candidates.

Origin of Structure in the Universe: quantum fluctuations in inflation and density perturbations; growth of inhomogeneities in a pressureless universe; growth of inhomogeneities in a radiation-dominated universe; the role of dark matter.

Temperature Fluctuations in the Cosmic Microwave Background: measuring the fluctuations; the Sachs-Wolfe effect; fluctuations on large and small angular scales; survey of the experiments; measurement of the density parameter.

Course Notes

  • 1. The Observable Universe (pdf)

  • 2. The Cosmological Equations (pdf)

  • 3. Solving the Cosmological Equations (pdf)

  • 4. Physical Cosmology I (pdf)

  • 5. Physical Cosmology II (pdf)

  • 6. Distance Scales and the Cosmological Constant (pdf)

  • 7. Early Universe I (pdf)

  • 8. Early Universe II (pdf)

  • 9. Successes and Problems with the Hot Big Bang Model (pdf)

  • 11. Inflationary Cosmology (pdf)

  • 10. Dark Matter (pdf)

  • 12. Origin of Large-Scale Structure (pdf)

  • 13. Anisotropies in the Cosmic Microwave Background (pdf)



    • Problem Sheets

  • Problem Set 1 (pdf)

  • Problem Set 2 (pdf)

  • Problem Set 3 (pdf)

  • Problem Set 4 (pdf)

  • Problem Set 5 (pdf)

  • Problem Set 6 (pdf)

  • Problem Set 7 (pdf)

  • Problem Set 8 (pdf)



    • Books

    Cosmology is a broad field and we will only be able to look at particular aspects of the subject in this course. There are a wide range of books on the market, but some care should be taken in choosing which one(s) to buy. Many focus on specific topics in considerably more detail than we will be able to go into and so they may appear difficult at first sight. However, you should persevere as background reading is important in a course of this nature. One of the best reasons for looking at more than one book at a time is that different authors often treat a given topic in different ways, and you may find one style more helpful than another. I'm reluctant to recommend a single text for this course, as no book really covers all of the material at the right level. Having said that, I found that I referred to the books by Madsen, Kolb & Turner and Coles & Lucchin most frequently when preparing lectures. The campus library stocks at least one copy of all these books, although some are restricted to one week loan.

    A. Liddle, An Introduction to Modern Cosmology Wiley, 1999, ISBN 0471987581.

    A very gentle introduction to the field with almost no mathematics. Intended for undergraduates, it may be helpful if you have no previous background in cosmology, but it does not by itself provide enough detail for this course. Its main advantage is that covers the main topics of relevance to modern cosmology.

    J. F. Harvey & K. A. Holcomb, Foundations of Modern Cosmology, OUP, 1998, ISBN 0195104978.

    A very descriptive, non--mathematical account of modern cosmology and the big bang. Another gentle introduction

    M. S. Madsen, The Dynamic Cosmos, Chapman & Hall, 1995, ISBN 0412623005.

    Intended for final--year undergraduates, this covers most of the topics relevant to modern cosmology and has a more mathematical approach. It provides a good introduction to this course.

    J. N. Islam, An Introduction to Mathematical Cosmology, Cambridge, 1992, ISBN 0521499739.

    This is more advanced than the books by Liddle and Madsen. Although parts of it focus on aspects of general relativity, about half of it is directly relevant to topics we cover.

    E. W. Kolb & M. S. Turner, The Early Universe, Addison--Wesley, 1990, ISBN 0201116030.

    A classic graduate textbook on the early universe. Although some parts of it are a little dated, the sections relevant to this course have stood the test of time, especially the chapters on physical cosmology and the big bang model. Although quite mathematical in places, I used this book a lot when preparing the course.

    P. Coles & F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure, Wiley, 1995, ISBN 0471489093.

    This is another excellent graduate textbook. Its emphasis is on models of large--scale structure as the authors are physical, rather than mathematical, cosmologists. The first half contains much of what you need to know and is pitched at about the right level for the course.

    J. A. Peacock, Cosmological Physics, CUP, 1999, ISBN 0521422701.

    This is an advanced text and discusses a vast array of cosmological topics in great detail, certainly more than we will be able to cover. The level is probably better suited to students who are setting out on their PhD studies. However, with a bit of work, you would benefit from having a look at this book, as parts of it are certainly accessible.

    P. J. E. Peebles, Principles of Physical Cosmology, Princeton University Press, 1993, ISBN 0691019339.

    This is another advanced book, providing a full survey of current issues in cosmology at a somewhat specialized level. Again, parts of it should be accessible and are worth looking at.

    A. R. Liddle & D. H. Lyth, Cosmological Inflation and Large--Scale Structure, CUP, 2000, ISBN 0521575982.

    This book specialises, as its title suggests, on inflation and structure formation. It evolved out of a technical review article and gives an advanced treatment of current issues in this field. Worth dipping into if you are particularly interested in the physical motivation and current status of inflationary cosmology.

    Past Exams

  • Exam 2009 (pdf)

  • Exam 2010 (pdf)



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