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 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/level5/March01/Carroll3/Carroll8.html

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

The following forum members have contributed to this FAQ:
bcrowell
George Jones
jim mcnamara
marcus
PAllen
tiny-tim
vela

FAQ: Is the Universe Finite or Infinite?

1. What are the three types of cosmological models?
   • The three types of cosmological models are:
     • Open Universe: Negative spatial curvature with infinite spatial volume.
     • Flat Universe: Zero spatial curvature with infinite spatial volume.
     • Closed Universe: Positive spatial curvature with finite spatial volume, resembling the three-dimensional analog of a sphere.
2. Can we determine if the universe is finite or infinite?
   • The finiteness or infiniteness of the universe cannot be determined by logic or theory alone. While all three models are solutions to Einstein’s field equations, observational evidence is needed to decide which model best describes our universe.
3. What do current observations say about the universe’s curvature?
   • Observations of the cosmic microwave background (CMB) suggest that the universe is very nearly flat. However, uncertainties in the curvature measurements leave room for both slightly positive and slightly negative curvature, keeping the question of the universe’s finiteness open.
4. What is the difference between the “universe” and the “observable universe”?
   • The observable universe refers to the portion of the universe that we can see or detect, limited by the finite time light has traveled since the Big Bang. It has a finite volume. The term “universe,” however, encompasses all of existence and could be finite or infinite, depending on its curvature and topology.
5. Why is a perfectly flat universe considered a special case?
   • A perfectly flat universe lies at the precise boundary between open and closed models. It represents a finely tuned condition that is mathematically possible but less general compared to the open and closed scenarios. This makes it a special and unique case among cosmological models.