1. 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. You should work your way through this syllabus, making yourself a set of notes as you go. Remember that you will be able to take these notes into the final examination with you. A set of self-test problems, with solutions, is also provided. You can use these to assess your understanding of the unit. Finally, in week 3, we will have a discussion class on Cosmological  Concepts.

You could spend an almost unlimited amount of time reading and constructing your notes for this unit. This would be a very bad idea, and you will have to be disciplined and well-organised. As a guide to the time you should spend, note that each lecture course is assumed to involve a total of 100 student "effort hours", of which approximately 25 hours might be used for exam revision on a typical course. In the case of Observational Cosmology, 30% of the credit is awarded for three assessed exercises, and it is assumed that you might spend 4 hours on each of these. The exam has been shortened to 90 minutes as a result. A reasonable allocation of study time for each unit is therefore about 12 hours (plus the lectures for the unit). Unit 1 is comparatively straightforward, so you might want to contain yourself to around 10 hours. This time should be used to (i) research the material using the guide in section 2, (ii)compile a concise set of notes (perhaps 10-15 sides for this unit),(iii)check your understanding with the self-test problems, and (iv) prepare for the discussion class (~1 hour). (The topics for discussion at the class are given at the end of this sheet.)

Remember to bring the notes you have made from your reading to the lectures and discussion classes. You will need them.

2. Syllabus & sources

In this unit we will introduce some concepts but mostly we will look at the basic observational evidence supporting the basic Hot Big Bang picture which is now accepted by almost all cosmologists. The three most important planks are the expansion of the universe, the cosmic microwave background, and the evidence from the abundance of the light elements which are believed to have been synthesised in the hot early Universe. I suggest that you research these in the order given below:
 

Topic	Sources	Comments
Introduction to observations     Galaxies, sizes, distances      Observations at different wavelengths	L1(2.1 & 2.2) , RR(1.1 to 1.4) L2(2.1 & 2.2)
Redshift     Definition      Origins of Doppler shifts	L1(2.4), RR(3.3 & 7.2) L2(2.4)	More advanced treatments are given in L2(A2.1) and RR(7.4), but you are not yet ready for these.
Hubble expansion     Concept; observations; receding galaxies	L1(2.4), NW(Part 1), RR(3.3) L2(2.4)
Comoving frame and peculiar velocities     Concept of co-movement      Galaxy motions ; effect on redshifts	NW(Part 1) , RR(3.3 & 4.1)
Observed isotropy and homogeneity of the Universe;  galaxy distribution; Cosmological Principle      Meaning of isotropy & homogeneity       Supporting observations      Cosmological (Copernican) principle, cosmic time	L1(1 & 2.3), L2(1 & 2.3)RR(3.4, 3.5 & 4.2), NW(Part 1)	See especially the plot of density fluctuation amplitude againt size scale in NW.
Distance scale and value of H0          Methods of  measuring distances        The distance ladder        Best current value of Ho	RR(3.2 & 3.3),  NW(Distances)	The most important methods are:  Parallax, Main Sequence fitting, Cepheids and RR-Lyraes,  Supernovae, Tully-Fisher
Cosmic microwave background       Observed  temperature, isotropy, spectrum       Origin  & implications       Dipole	NW(Part 1), RR(3.4 & 5.5), L1(2.5.2 & 9.1), L2(2.5.2 & 10.1)	Don't worry too much about microwave background fluctuations at this stage.
Cosmic nucleosynthesis - the abundance of the light elements       See the guidance	L1(11 to 11.2),  unit 1 lecture    L2(12 to 12.2) MW,  RR(5.3), Thuan & Izotov	Important guidance is given here.  Note that Fig 11.1 of Liddle(1st edition) has densities on the x-axis in cgs units. This is fixed in the 2nd edition

Notes
1.  Key: RR=Rowan-Robinson (4th edition), L1=Liddle(1st edition), L2=Liddle(2nd edition), NW=Ned Wright's pages , MW=Martin White's pages - relevant sections are given in brackets. In most cases, the 3rd edition of Rowan-Robinson is very similar to the 4th.
2. The topics listed are not of equal size (the last 3 are the largest).
3. References given are not by any means the only ones (e.g. check out some of the links and references on the Home Page), but they should provide a reasonable treatment.
4. 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.

3. Self-test problems

Use these questions as you proceed through the unit, to judge whether your coverage of the material and level of understanding are adequate. Answers are just a click away, via the      button, but you will greatly reduce the diagnostic value of the questions if you look at the solutions before making a serious attempt to answer the question yourself.

1. Calculate the Doppler shifts which would arise from (i) the rotation of the Earth, (ii) the Earth's orbital motion, (iii) the solar motion around the Galaxy 
2. If a spectrograph operates in the band 5000-9000 Angstrom, over what redshift range will the H_alpha(6563 A) and H_beta(4861 A) Balmer lines from galaxies both fall within the bandpass? (It is hard to determine a redshift with a single line!) 
3. If typical peculiar velocities for galaxies are 500 km/s, how far away must a galaxy be for its velocity and distance to constrain H₀ to 10%, assuming (unrealistically) perfect measurements of v and d? 
4. What is a good way  to determine whether one is in a comoving frame? (Hint:  think about  background  radiation) 
5. What are the main observations which support the Cosmological Principle (ie isotropy & homogeity)? 
6. The accompanying figure shows a sketch of the Hertzsprung-Russell diagrams for two star clusters. The Main Sequence and MS turnoff can be seen. 

(i)Which cluster is more distant?,
(ii) Approximately how much more distant is it?,
(iii) What can you say about the ages of the two clusters? 
7. If the period:luminosity relation of Cepheids is given by M _V=-2.76(logP-1.0)-4.16, where P is the period in days, calculate the distances to two galaxies which contain Cepheids with identical mean apparent magnitudes, m_V=24.5, but with periods of 37 and 81 days, respectively. 
8. How large a spatial scale must one consider before typical fluctuations in the mean density of the Universe drop to ~10%?  (Hint: look in Ned Wright's cosmology tutorial.)     
9. What is the resolution of Olber's paradox? Is there more than one effect at work?     
10. What is the energy density of the CMB radiation? Compare this with the energy density of sunlight at the Earth. 
11. Why are the predictions of nucleosynthesis important in the Big Bang model? 
12. Why do the nucleosynthesis results rule out there being sufficient baryons to close the Universe? 

a) Lecture:  The Hot Big Bang - overview and evidence

After a brief introduction to the way the course as a whole will work, I will outline the main lines of evidence which have led to the acceptance of the Big Bang by almost all astronomers, and show some recents results on the distribution of galaxies.

b)  Discussion class: Cosmological Concepts #1

This class is in week 2, by which time you should be half way through the unit.  You will work in groups on questions designed to stimulate discussion on various conceptual  issues, such as : 

   How large is the Universe?
   Why doesn't Hubble's law violate the cosmological  principle?
   Where was the Big Bang?

You will get more out of the session if you think about these questions in advance of the class. Discuss them with your friends!

Send comments or suggestions on these pages to Trevor Ponman
Last updated  2 October 2008