A simple quantum cosmology

Abstract

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 h, c, G and the proton mass. 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 the Hubble constant is 65 km/sec Mpc, the energy density of the scalar field after inflation results in Omega-sub-Lambda = 0.68, in agreement with recent astrophysical observations.