How was space formed?
The short answer: we don't know.
But what exactly is it that we do and don't know? It all boils down to first asking: "What is space?" To answer that, let me summarize the essence of the two greatest theories of 20th century physics in one sentence each.
Relativity: Space and time are a relational structure between things.
Quantum mechanics: But what are things?
According to relativity, space and time do not have a separate existence from the material objects in the universe. This is very different to the old idea of Isaac Newton that axes of space and time exist separately from the things in the Universe. We have known for over 100 years that Newton was wrong on this point. Fixed axes can only be used to accurately describe the motion of objects on small scales. Even then measurements still involve comparisons of physical rulers and clocks.
Space and time are a set of rules which tell us how measurements made by the rulers and clocks of one observer relate to those of any other observer. For observers who travel with respect to each other at nearly the speed of light the rules of special relativity are very different to Newton's mechanics. General relativity tells us that on large scales space and time are curved in such a way that there does not have to be one single set of space-time axes.
The Universe began as a hot dense plasma in explosion. But the Big Bang was not an explosion in a pre-existing space. Space just means the distances between the particles, so space came into existence as average distances between the first particles increased. On average this expansion was the same everywhere; the "Big Bang" did not occur from a single point but about every point at the same time.
Gravity is attractive and slows down the rate at which distances between objects increase. In the densest regions gravity has completely reversed the expansion of space and made particles collapse together to form structures: galaxies, stars, planets and everything you see outside your window. Space on these scales is not expanding. However, on very large scales the distances between clusters of galaxies are still increasing, but at a slower rate than when the Universe began. That is what we mean by the expansion of the Universe; in a very real sense empty space is still being formed today. But "expanding space" is not something that exists in its own right; it only has a meaning as the increasing distances between clusters of galaxies. Space is nothing; there's just more of it as time goes by!
Since space is just a measure of the distances between things, asking how space first formed is the same as asking: How did the first things form? Or, how did the universe form? As you squeeze more and more energy into a smaller and smaller volume then the nature of what things are changes, as does the whole notion of what we mean by distances. It gets mixed up with all the fuzziness of Heisenberg's Uncertainty Principle, which underlies quantum mechanics.
There are hundreds of speculative theories, known as inflationary models, which attempt to describe the Universe in its first moments. New measurements by the BICEP2 telescope announced last month, and from the Planck satellite, will begin to nail such theories down this year.
Professor David Wiltshire
Department of Physics and Astronomy
University of Canterbury