[jnb]

"What's beyond space?" is a meaningless question in the same way that "what's north of the north pole?" is a meaningless question.

Broadly speaking the big bang is the point at which everything is created including all energy, all matter and all of space and time. As of the big bang space itself has been expanding and carrying all the matter and energy within it. It's not that its an area of space into which things expand instead it is all of space within which there are things.

If you want an analogy imagine a balloon on which are drawn tiny points representing all the galaxies. As the balloon expands all the galaxies rush away from one another but no one point on the balloon's surface is the centre from which they all rush away and there is no meaningful concept of what the balloon is expanding into (ignoring the fact that in the analogy the balloon expands into a third dimension but all analogies break down if pushed too far). There is no "beyond" space just as there is no "before" the big bang and there is no north of the north pole.

It might not be intuitive but it appears to be the way it works.