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The Annual Lewis Elton Lecture - 2012 According to currently standard cosmology, the universe started with a Big Bang, immediately followed by a fleeting moment of exponential expansion, called "inflation". Following this it settled down to a more sedate expansion, but due to what is called "dark energy", it is currently commencing a second period of exponential expansion that is expected to continue indefinitely. In this talk I describe an alternative idea, which argues that this picture provides merely one aeon of a continual succession of such aeons. The Universe never collapses in this model, but the remote future of each aeon becomes, when infinitely scaled down, the big bang of the next. Collisions between supermassive black holes in the aeon previous to ours would, according to my model, provide disturbances that should be just about observable in the cosmic microwave background of our own aeon. In this talk I shall describe evidence indicating that these disturbances may actually be present, and possibly providing us with some hint of what the aeon prior to ours may actually have been like. The talk will be largely free of equations, depending mostly on pictures, but a brief summary of the equations needed for the theory will be provided at the end. Brief biography: Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe. He is renowned for his contributions to general relativity and cosmology. He is also a recreational mathematician and philosopher.