The evolution of the Universe, from the Big Bang to its ultimate fate, can be described in terms of General Relativity: Einstein's theory in which gravity is modelled by curved space-time. The project will study this model of cosmology. Einstein's equations are tricky to solve in general, but the simplest cosmological model assumes a high degree of symmetry, and boils down to an ordinary differential equation, called the Friedmann equation, which is much easier to handle.

The project will begin by investigating various solutions of the Friedmann equation, corresponding to different evolutions of the universe. The simplest cases can be solved exactly, but you will also need to implement some straightforward numerical solutions by computer. A later part of your work will be to put together a concise account of the relevant parts of general relativity, explaining the background and in particular how this model of cosmology arose.

For an accessible introduction to the topic, take a look at this article about the Friedmann equation. It includes some of the physics background; the project will however focus on the mathematics.