9.1 Curved space
Curved space is hard to imagine, but you can use the analogy of a curved surface. A sphere is a familiar example of a curved surface and is said to have ‘positive curvature’. If space is positively curved, like the surface of a sphere, then it is finite and we have a ‘closed’ universe. If space has zero curvature, like a flat surface, then it is infinite and we have a borderline ‘open’ universe.
It is also possible for space to have a negative curvature, in which case it will also be infinite and open. An analogy for this is harder to visualise – but a popular potato snack comes close. You just have to imagine the edges extending to infinity!
A finite universe need not have an edge. Consider the surface of the Earth – it is finite, and its surface area can be measured precisely. And yet you can travel any distance across the Earth’s surface, in any direction, and you’ll never reach an edge. The same may apply if the universe is closed and positively curved. Despite having a finite and precisely measurable volume, you could travel around and never encounter an edge.
But this is not the whole story, of course. If you travel far enough across the surface of the Earth, you’ll eventually return to the point from where you started. The same thing could happen in a closed universe. Given enough time, a starship sent out in a straight line to explore the depths of space could eventually find itself back on Earth. Now, we’re not likely to embark on such an expedition anytime soon, but one thing does travel fast enough through space to manage it, and that’s light.