| The present universe has Ωm0 = 0.23 and Ωr0 = 8.4 × 10-5. Calculate the redshift z at which Ωm = Ωr (the epoch of matter-radiation equality). | [2] |
| First recall the a-dependence of the two Ω terms: H(t)2Ω(t) = H02Ω0/an, where n = 3 for matter and n = 4 for radiation. Use this to determine the value of a for which Ωm/Ωr = 1 (converting to a ratio gets rid of the factors of H), and then use a = 1/(1+z) to convert to z. | |
| The differential equation for structure growth shows that density perturbations should grow ∝ a in a matter-dominated universe. Explain why, despite this, one might expect that structures would not start to grow until the epoch of recombination at z ∼ 1100. | [2] |
| This is bookwork. You need two points for the two marks: first explain what prevents structures from collapsing under gravity, then explain why recombination is significant. | |
| How does the recognition that most of the matter in the universe is non-baryonic cold dark matter affect the growth of structure? | [3] |
| You need to cover two different issues here: what is the significance of the fact that the dark matter is non-baryonic, and what is the significance of its being cold? |
(2006 Resit Q7(b).)