  Astrophysical observations indicate the expansion of the universe is
accelerating. Applying the holographic entropy conjecture to the cosmological
horizon in an accelerating universe suggests the universe has only a finite
number of degrees of freedom. This is consistent with a closed universe arising
from a quantum fluctuation, with zero total quantum numbers. If space-time has
eleven dimensions, and the universe began as a closed force-symmetric
ten-dimensional space with characteristic dimension L, seven of the space
dimensions must have collapsed to generate the three large space dimensions we
see. The holographic conjecture then suggests the initial length scale L must
be roughly twenty orders of magnitude larger than the Planck length.
Accordingly, the nuclear force must be roughly forty orders of magnitude
stronger than gravity, possibly resolving the force hierarchy problem. A
wavefunction for the radius of curvature of the universe can be obtained from
the Schrodinger equation derived by Elbaz and Novello. The product of this
wavefunction and its complex conjugate can be interpreted as the probability
density for finding a given radius of curvature in one of the infinity of
measurements of the radius of curvature possible (in principle) at any location
in a homogeneous isotropic universe.
