Using the relic dark energy hypothesis to investigate the physics of   cosmological expansion
  We use the trans Plankian hypothesis about Dark energy as outlined by Mercini et al to investigate some of the physics of cosmological expansion. We find that a parametric oscillator equation frequency we can use leads to a time dependent frequency whose dispersion relationship behavior mimics the Epstein functions used by Mercini et al in the initial phases of cosmological expansion, but that it is very difficult to meet the trans Planckian assumptions of a vanishing of this same frequency with known physics at ultra high momentum values. So being the case, a numerical algorithm used to re construct the scale factor for cosmological expansion is proposed which is to re construct more of the physics of the Trans-Planckian hypothesis in Trans-Planckian momentum values 
A.W.Beckwith