Project:

In 2010 Sir Prof. Roger Penrose released a book detailing a revolutionary new view of the universe. He showed that mathematically one can join our expanding universe in the infinite future to the big bang of the past. Thus if you were a photon, or graviton, or anything with zero rest-mass, you could travel infinitely far in time (zero rest-mass fields have no notion of time) and end up propagating through the big bang and into another iteration of our universe. These iterations of our universe have been coined "aeons" and the theory is called Conformal Cyclic Cosmology (CCC).
The aim of this project is to investigate this theory in more detail. Which particular area is up to the student and can be purely mathematical or have a numerical component. Examples could include: how does one uniquely fix the conformal factor at the crossover? What does gravitational radiation look like when propagated from one aeon to the next? What are the structure of the CCC equations for simple asymptotically de-Sitter space-times; are they wellposed?