The Finite Universe HypothesisFinite Universe is the hypothesis that:
If the universe is spatially finite, the question arises about how big it is.
A spatially finite universe does not require that there be an "edge". Rather periodic boundary conditions would be employed.
If periodic boundary conditions are used, it seems quite possible that the universe is much smaller than what would be suggested by the apparent diameter of the visible universe.
This would be rather difficult to detect experimentally - so it is not very suprising that such a regularity has not yet been identified.
The problem is that - when you look out into space, you are looking backwards in time. Consequently you don't see exactly the same configurations repeated - in a regular pattern - but rather snapshots of the earlier evolution of the system at varying times.
This explains why you don't necessarily see much the same things in the distance when you look in diametrically opposed directions.
What about the fact that distant galaxies are all receeding from us? In a finite universe would we not see as many approaching as receeding?
There are several possible ways this could be resolved:
Other observations suggest that there are problems with the redshift data. [Redshift Quantization]is often invoked in this connection. To quote from there:
Such notions cast doubt on the conventional red-shift interpretation.
Having said this, evidence for universal expansion is fairly well established. Such evidence suggests that - if the universe is finite, it is comparable in size to the visible universe.
Finite Universe has some explanatory power. It explains spatial homogeneity - which otherwise seems mysterious - despite the attempts of inflationary scenarios to explain it.
Also it is consistent with Berkeley and Mach's hypothesis that all the matter in the universe is collectively responsible for experienced inertia.
Then there's some work in quantum cosmology - which seems to suggest a low- volume universe is more probable than a high-volume one, and an infinite universe would have zero probability of coming into existence.
It appears that testing the theory that the universe has periodic boundary conditions - and is smaller than the visible universe - would probably require a comprehensive statistical analysis of the presence of he background radition - or very long-lived objects to test.
The National Aeronautics and Space Administration's Microwave Anisotropy Probe (MAP) has now been launched - and seems likely to produce results relevant to this question shortly. The first results are expected in 2002.
This issue is currently being seriously discussed by cosmolgists.