It is notoriously difficult to reconcile the two most basic frameworks of the fundamental laws of nature, namely general relativity and quantum theory. The first describes gravity and how it influences space and time—you could say it relates to the large—while the second characterises the behaviour of all known elementary particles—relating to the small. In order to understand the big bang, they will have to be combined.
Why is it so hard to unify gravity and quantum theory? To illustrate this, it helps to recall the bizarreness of the quantum world. According to quantum theory, nature explores all possibilities to determine the probability with which an event occurs. So when a ball is thrown, absolutely all conceivable trajectories are considered, but only a few weigh in significantly. (In the case of the ball, in fact, only the familiar classical trajectory is relevant.) When applied to space-time, however, it gets tricky. All possible space-time evolutions must be considered, but the trouble is that on tiny scales, the fabric of space-time tends to become very messy.
Faced with those difficulties, James Hartle and Stephen Hawking put forth their "no-boundary" proposal. Their highly elegant idea was that one should not consider all possible space-time evolutions but only those that have a smooth initial space-time geometry. You can picture this by imagining that the early universe would have been rounded off like the surface of a ball, not only in space but also in time. Time would have had no edge—hence the name of the proposal. This idea has two highly desirable consequences. The first is that it might actually allow one to calculate things, as the geometries are forced to be smooth and, thus tractable, initially. The second is that by providing a theory of what effectively replaces the big bang, we would know the most likely starting point of the universe. Still, until recently, it remained difficult to calculate the true consequences of this idea. Despite the simplification of having to deal only with these "no-boundary" geometries, it is not easy to calculate how all the different space-time evolutions sum up, or how to determine which ones are the most important.
About seven years ago, my collaborators Job Feldbrugge and Neil Turok, both of the Perimeter Institute in Canada, and I realised that there exists a mathematical framework, called Picard-Lefschetz theory, which has been continuously developed by mathematicians over the last 100 years and that is perfectly suited to this kind of calculation. It is only over the last decade that physicists have become aware of its existence. Using these methods, we encountered a surprise. When we imposed the condition that the universe starts from zero size, the resulting universes inevitably developed large fluctuations. In other words, the geometries that develop strong irregularities contributed the most to the final answer. This implies that one would get a highly crumpled universe popping out of nothing and presumably collapsing again right away, rather than expanding into the vast universe we know.
This was the puzzling situation we found ourselves in at the beginning of this project. The main aim of the project was to see if either the no-boundary idea must be reformulated so as to work, or to look for alternative descriptions of the big bang and the emergence of space and time. In the end, we did both.
