Is the universe infinite, or finite? How big is the universe?
We know that the universe is expanding because, with some nearby exceptions, almost every galaxy in the universe is moving away from us and from one another. Not only that, but very distant galaxies appear to be receding even more quickly, evidence that the universe is expanding at an increasing rate.
Observations of various times in the universe suggest that, for the first several billion years, the universe’s expansion slowed — but then roughly 8 billion years ago, expansion began accelerating. If the acceleration continues (which seems likely), the universe will never slow its expansion or re-collapse. This corresponds to the idea of a “flat” universe, which is currently the most accepted model.
But a spatially flat universe can be characteristic of either a finite or an infinite universe. When we say that space is “flat,” we mean it obeys Euclidean geometry: parallel lines never intersect, and the angles of a triangle always add up to 180 degrees. We can imagine the universe in two dimensions as a plane, which is flat and infinite (like an infinite piece of paper). But we can also imagine taking that paper and rolling it into a cylinder, then rolling it again into a torus (doughnut shape). The surface of the torus is spatially flat, like the piece of paper, but finite. However, with expansion, it is possible that even if the universe just has a very large volume now, it will reach infinite volume in the infinite future.
The Size of the Observable Universe
The space that we can observe, on the other hand, does have a definite size. Because the universe was born 13.8 billion years ago, we can only observe objects whose light has traveled at most 13.8 billion years to reach Earth. This portion of the universe is called the observable universe, and it’s the only part of the universe we can know anything about.
But due to the universe’s expansion, the radius of the observable universe is not 13.8 billion light-years. Current estimates instead set its radius at about 46 billion light-years, an estimate made in co-moving coordinates, which account for the expansion of the universe. As the universe ages, the size of the observable universe will continue to expand.
Further reading: “Is the universe finite or infinite? An interview with Joseph Silk.”