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. More detailed advice on how to approach the work is given in the introduction to Unit 1 , and will not be repeated here. You should aim to spend about 12 hours on the unit, plus a further 4 hours for the assessed exercise (quite a lot of which relates back to Unit 2). This unit is conceptually less challenging than the last one, but parts of it are really not covered at all adequately by either of the course books, and the field of galaxy formation is moving very fast. My lecture is intended to introduce you to the topic of structure formation.

2. Syllabus & sources

In this unit we study the major stages in the evolution of the Universe after the Big Bang, taking them in chronological order. We pass quickly over the exotic early phases, which will be examined in more detail in the 4th Year course Extreme Environments and the Early Universe, but look at the emergence of macroscopic structures. Notes from section 9 of the Year 2 Structure in the Universe course give a useful outline of structure formation, and the online copy of Bothun's book provides useful detailed discussion, to supplement the rather sketchy treatment of some of these issues in Liddle and Rowan-Robinson. Finally, you should spend a little time browsing through some of the links to cosmological simulation pages, to get a feel for the impact which such studies are making on our understanding of the evolution of the Universe - I will say more about this in the Unit 3 lecture. This lecture (apart from its simulations) can be accessed as a web page here (this works reasonably with the Mozilla browser, so try this if Internet Explorer mangles it for you) or as a single pdf file here.
 

Topic	Sources	Comments
Particle  horizon:     Concept  - the observable Universe	RR(4.10)	The particle horizon is often referred to simply as "the horizon".
Horizon and flatness problems:    Problems of the Big Bang model:    Flatness - why is Omega close to 1 ?     Horizon  - unconnected regions have same CMB temperature	L(12.1),  RR(p.161-2) L2(13.1)
Inflation:     Early rapid exponential expansion      Solves horizon & flatness problems      May be due to a phase of high vacuum energy density	L(12.2-12.5), RR(5.4),  NW(Part 4) L2(13.2-13.5)	See sections I-III of the  Guth paper for more detail
Evolution of density and temperature:     Effect of expansion on density and temperature     Differing behaviour of matter & radiation - matter and radiation dominated eras	RR(5.1 & 5.2) , L(9.1, 10) L2(10.1,11)	See especially RR Figs. 5.2 & 5.3
Cosmic nucleosynthesis:      Key reactions      Origin of the helium fraction     Why are only light elements synthesised?	RR(5.3), L(11) L2(12)	Add to  your notes from Unit 1 - this time tracing the key reaction stages.
Recombination (decoupling):     What is this, when and why did it happen?	RR(5.2), L(9.3) , L2(10.3-10.4)
Growth of structure     From CMB fluctuations to today's galaxies      Growth of density perturbations     Collapse and virialisation     Hierarchical merging     Jeans mass   and the effects of pressure  on baryons	RR(5.5,6.1-6.2), L(13), L2(A5.2, A5.4), B(3.1,  4.1, 5.1-5.3), Unit 3 lecture	Major section - see detailed guidance here.
Galaxy formation     Cooling of baryons     Monolithic collapse and hierarchical models	Unit 3 lecture, RR(2.5) Detailed treatments in papers by Ellis (observational), and Baugh and Cole (theoretical modelling).	R-R gives only a little on this important topic, and Liddle almost nothing. The papers referred to here are more detailed than you need, but you could usefully skim through some of them.
Cosmological simulations     Growth of large-scale structure depends on  cosmological  parameters	Hubble volume , VIRGO, Local volume	Note that some simulations include only dark matter.

Notes
1.  Key: RR=Rowan-Robinson, L=Liddle (L2=2nd edition), NW=Ned Wright's pages, B=Bothun - relevant sections are given in brackets.
2. The topics listed are not of equal size.
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).
4. For the more complex topics 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. What is the redshift of a galaxy on our own "particle horizon"? How does the observed redshift of such a galaxy change with time, and why?  
2. If Omega were 0.4 at the present epoch, how close would it have been to unity at a redshift of 1000, assuming that a grows as t^2/3 (i.e. as a for a fairly flat matter-dominated universe)? 
3. The binding energy of the electron in a hydrogen atom is 13.6 eV.

(a) Calculate the temperature at which the mean blackbody photon energy has this value.
(b) At what redshift would the cosmic CMB radiation have this temperature?
(c) Why is the blackbody assumption a good one?
(d) Compare the redshift you calculated with that at which decoupling of matter and radiation actually occurs. What might account for the difference? 
4. What motivates the strange idea of cosmic inflation? 
5. In what way does the vacuum energy which drives inflation differ from that associated with Lambda? 
6. If the lifetime of free neutrons were 100 s, rather than ~1000 s, what would be the main effect on the abundances of the elements? 
7. Why are elements heavier than Li not synthesised in significant quantities in the Big Bang? 
8. Why should density fluctuations in the early Universe lead to temperature fluctuations in the CMB? Hint: look at section 3.1 in Bothun.
9. How would the Jeans Mass evolve with a after recombination, if the gas expands adiabatically with the Universe? 
10. What effect do you think the cosmological constant will have on the growth rate of density perturbations on scales of galaxies and clusters? 
11. Why is it reasonable to adopt the growth rate of density fluctuations for an Omega_matter=1 universe for much of the history of our Universe?
    Why does this fail at low redshift, and what observational consequences do you think this might have? 
12. What difference would you expect to observe between two systems of the same mass which virialised at z=2 and z=0 respectively? 
13. How would a typical spiral galaxy like the Milky Way (with a bulge and disc) be assembled according to current ideas about hierarchical galaxy formation? 
14. Why are theorists much more confident of their ability to simulate and  model the evolution of dark matter than of baryons, despite our ignorance of what dark matter actually consists of? 

a) Lecture: The Growth of Cosmic Structure

In this Powerpoint lecture, I will describe the way in which structures form in an expanding Universe, and show some examples of cosmological simulations of structure formation. We will then look at the process of galaxy formation and the most popular approaches to modelling this crucial aspect of structure formation.

b) Discussion class: Cosmological Concepts #3

c) Assessed exercise:

The second assessed exercise for third year students is available here.
It must be completed and returned to the Teaching Office by 4pm on Monday Nov.24th.