Gresham College presents The Annual Sir Thomas Gresham Lecture 2022 with Sir Roger Penrose, the Emeritus Rouse Ball Professor of Mathematics at the University of Oxford.

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The “singularity theorems” of the 1960s demonstrated that large enough celestial bodies, or collections of such bodies, would, collapse gravitationally, to “singularities”, where the equations and assumptions of Einstein’s general relativity cannot be mathematically continued. Such singularities are expected to lie deep within what we now call black holes. Similar arguments (largely by Stephen Hawking) apply also to the “Big-Bang” picture of the origin of the universe, but whose singularity has a profound structural difference, resulting in the 2nd law of thermodynamics, whereby “randomness” in the universe increases with time. It is hard to see how any ordinary procedures of “quantization” of Einstein’s theory can resolve this contrasting singularity conundrum,

Yet, a deeper understanding of the special nature of the Big Bang is obtained from the perspective of conformal geometry, removing the distinction between “big” and “small, and whereby the Big-Bang singularity, unlike those in black holes, becomes non-singular, and can be regarded as the conformal continuation of a previous “cosmic aeon”, leading to the picture of conformal cyclic cosmology (CCC) according to which the entire universe consists of a succession of such cosmic aeons, each of whose big bang is the conformal continuation of the remote future of a previous aeon. Some recently observed effects provide some remarkable support for this CCC picture.