Astrophysical observations indicate the universe is asymptotic to a de Sitter space with vacuum energy density \Omega _ { A } = 0.7 .
Then , since H _ { 0 } \approx 65 km sec ^ { -1 } Mpc ^ { -1 } , our universe has only about 10 ^ { 122 } degrees of freedom .
A finite number of degrees of freedom 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 length l , seven of the space dimensions must have collapsed to generate the three large space dimensions we perceive .
The holographic entropy 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 about forty orders of magnitude stronger than gravity , possibly resolving the force heirarchy problem .
A wavefunction for the radius of curvature of the universe can be obtained from the Schrödinger 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 .