PX311 Relativistic Cosmology
Sample Examination Questions 2001-2
Dr Hyland lectured this course for many years to 2001, using a different choice of co-ordinates for the Robertson-Walker metric, as well as other differences of emphasis. The examination questions 1999-2001 remain broadly applicable to the present course, but you may encounter some mismatch in levels of detail.
A sample of new questions drafted by the present lecturer is provided below. Please note that these have not been subjected to examination procedures such as moderation (particularly as to length!) and external checking.
1. Discuss our understanding (at the level of the lectures!) of three of the following:
(a) The age of the Universe is of order 12 Gyr;
(b) Around 22-24% of baryonic matter is 4He;
(c) The Universe is full of microwave radiation with temperature about 2.8K;
(d) The experimental evidence for General Relativity.
[25]
2. State the Strong Equivalence Principle [2]
and show that this leads to the expectation that light rays should bend their paths in a gravitational field. [3]
The observed deflection of starlight by our sun is twice the value suggested by the Equivalence Principle: how do we understand this? [2]
Explain the terms Metric Tensor and Geodesic Motion. [4]
Indicate (without derivation) the form of equation of motion to which these lead in the non-relativistic limit [2] and hence sketch the considerations leading Einstein to
,[4]
explaining the physical significance of the objects on both sides of the equation.[2]
For the flat Robertson-Walker metric, . Hence assuming that , find two possible forms for when and give an interpretation of each. [Hint: for radiation]. [6]
3. Starting from the Robertson-Walker "metric" as
,
explain:
(a) what it gives; (b) the physical interpretation of the time co-ordinate here; (c) the interpretation of ; (d) the significance of , distinguishing particularly from . [8]
(e) For a light signal travelling at fixed and show that
. [3]
Assuming for simplicity that and , find
(f) the furthest distance at which past events could influence an event at time, ; [3]
(g) the furthest events (in terms of ) at time which can be "seen" by an observer at later time . [3]
(h) Explain the significance of your answers to (f) and (g) for the observed fluctuations in the Cosmic Microwave Background, [5] and in this context:
(i) what changes would you want to make to the assumed form of ? [3]
RCB 7-12-01