A simple and surprisingly realistic model of the origin of the universe can be developed using the Friedmann equation from general relativity , elementary quantum mechanics , and the experimental values of \hbar,c,G and the proton mass m _ { p } .
The model assumes there are N space dimensions ( with N > 6 ) , and the potential constraining the radius r of the invisible N - 3 compact dimensions varies as r ^ { 4 } .
In this model , the universe has zero total energy and is created from nothing .
There is no initial singularity .
If space-time is eleven dimensional , as required by M-theory , the scalar field corresponding to the size of the compact dimensions inflates the universe by about 26 orders of magnitude ( 60 e -folds ) .
If H _ { 0 } = 65 km sec ^ { -1 } Mpc ^ { -1 } , the energy density of the scalar field after inflation results in \Omega _ { \Lambda } = 0.68 , in agreement with recent astrophysical observations .