The role of quantum expansion in cosmic evolution
  A quantum expansion parameter, analogous to the Hubble parameter in cosmology, is defined for a free particle quantum wavefunction. By considering the universe as an initial single Gaussian quantum wavepacket whose mass is that of present-day observable universe and whose size is that of the Planck Length at the Planck Time, it is demonstrated that this quantum expansion parameter has a value at the present epoch of the same order as the value of the Hubble constant. The coincidence suggests examining the effect of including this type of quantum wave expansion in traditional general relativistic cosmology and a sample model illustrating this is presented here. Using standard Einstein-de Sitter cosmology ($\Omega$m = 1) it is found that cosmic acceleration (aka dark energy) arises naturally during cosmic history. The time at which the universe switched from deceleration to acceleration (observationally ~7 Gyr before the present epoch) yields a value for the mass of the wavepacket representing the universe at the Planck Time and its present age. This same mass may then be used to obtain a curve for the cosmic expansion rate versus z. This curve is well fit to observational data. The model is used also to obtain an estimate of the inflationary expansion factor. 
A. D. Ernest
astro-ph.CO gr-qc quant-ph