| In the context of the standard (pre-inflation) Big Bang model, explain what is meant by the following catch-phrases, and why they are described as "problems": | |
| (i) the horizon problem; | [2] |
| (ii) the flatness problem; | [2] |
| (iii) the monopole problem. | [2] |
| All of these are bookwork. One of the two marks is for the explanation of what the phrase means, and the other is for explaining why it is a problem. You are not asked for a quantitative explanation, so you don't need to do explicit calculations (though of course you can if you are confident!) | |
| Briefly explain the term "inflation", and explain why introducing a period of inflation solves the above problems. | [2] |
| More bookwork. Because you're only getting 2 marks, you should take the "briefly" seriously – details are not required. | |
| Inflation is generally modelled as a large positive cosmological constant. Show that in this model the expansion factor of the universe during inflation is given by a(t) = a(ti) exp[H(t – ti)], where ti is the time that inflation starts. If we assume that inflation starts at 10-35 s, ends at 10-33 s, and involves 100 e-foldings of expansion, what is the implied value of the cosmological constant Λ? | [3] |
| This question has two parts: deriving the "Λ-only" solution of the Friedmann equation, and putting in the numbers to determine Λ. The first part is stand-alone: if you knew you couldn't do it, but were happy with the rest of the question, you could opt to forfeit the 2 marks on offer and just go for the numerical bit at the end. |
(2005 Resit Q5(a) and (c).)