Is the universe finite, or is it infinite?

Greg Bernhardt

Is the universe finite, or is it infinite?

Standard cosmological models come in three flavors, open, flat, and closed,[Carroll] whose spatial curvatures are negative, zero, and positive. The open and flat types have infinite spatial volume. The closed one has finite spatial volume; spatially, it is the three-dimensional analog of the surface of a sphere. Since all three are solutions to the Einstein field equations, the finiteness or infiniteness of the universe is something that cannot be determined solely by logic but only by observation.

Current observations of the cosmic microwave background's anisotropy show that our universe is very nearly flat.[Komatsu] If it is exactly flat, then it is a special case lying on the boundary between the more general open and closed cases. However, the range of uncertainty in the curvature is wide enough to be consistent with either positive or negative curvature, so right now the finiteness or infiniteness of the universe is an open question.

Sometimes people use the word "universe" when they really mean "observable universe." The observable universe is finite in volume because light has only had a finite time to travel since the Big Bang.

[Carroll] Sean Carroll, "Lecture Notes on General Relativity," http://nedwww.ipac.caltech.edu/level.../Carroll8.html

[Komatsu] Komatsu et al., Astrophys. J. Suppl. 192(2011)18, http://arxiv.org/abs/1001.4538


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