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An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.
However, some models propose it could be finite but unbounded, [note 5] like a higher-dimensional analogue of the 2D surface of a sphere that is finite in area but has no edge. It is plausible that the galaxies within the observable universe represent only a minuscule fraction of the galaxies in the universe.
The possibility of a finite and unbounded universe does not imply that the universe is actually finite, or actually unbounded. There's simply no observational evidence to suggest that the universe is finite (or that it isn't), and no theoretical reason that it should be one way or the other. --Bowlhover 05:17, 23 March 2014 (UTC)
An expanding universe typically has a finite age. Light, and other particles, can have propagated only a finite distance. The comoving distance that such particles can have covered over the age of the universe is known as the particle horizon, and the region of the universe that lies within our particle horizon is known as the observable universe.
Due to the finite speed of light, we see more distant parts of the universe at earlier times. Due to the finite speed of light, there is a limit (known as the particle horizon) to how far light can travel over the age of the universe. The spatial region from which we can receive light is called the observable universe.
A universe that is finite in time and has a beginning is proposed by the Christian philosopher John Philoponus, who argues against the ancient Greek notion of an infinite past. Logical arguments supporting a finite universe are developed by the early Muslim philosopher Al-Kindi, the Jewish philosopher Saadia Gaon, and the Muslim theologian Al ...
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course ...
The Einstein model describes a static universe; space is finite and unbounded (analogous to the surface of a sphere, which has a finite area but no edges). However, this so-called Einstein model is unstable to small perturbations—it will eventually start to expand or contract. [5]