If space has positive curvature, there is more than enough mass to stop the present expansion of the universe.
The next type of surface has what is called positive curvature. This is best represented in two dimensions by the surface of a sphere. Remember, the 2-D creatures in this Universe don't see up or down, so they don't know that they are on a sphere.
A sphere is said to have positive curvature. However, if the average density of the universe is below the critical value, the surface curves like a saddle. It has negative curvature.
If the universe has positive curvature, then the number of galaxies increases with greater volume then decreases with very large volumes. Lines defining an angle spread out at first and then converge at great distances.
In this state, the expansion of the universe will eventually be reversed; it is characterized by positive curvature, being finite in extent but having no boundaries.
k=0 means that the 3-space t=constant is Euclidean (q0=1/2)
k=+1 is closed, with positive curvature (q0 > 1/2)
k=-1 is open with negative curvature (q0 < 1/2).
As described in the previous section, the total volume of a three-dimensional space with uniform positive curvature would be finite but possess no edges or boundaries (to be consistent with the first assumption).
A three-dimensional space whose geometry resembles that of the surface of a sphere and is said to have positive curvature. [Silk90]
Spica ...
First and most importantly, the length scale R of the universe can remain constant only if the universe is perfectly isotropic with positive curvature (k=1) and has one precise value of density everywhere, as first noted by Albert Einstein ...
 See also: Galaxies, Time, Universe, Mass, General Relativity
  
|
RSS
