We start where we use an inflaton value due to use of a scale factor
. Also we use
as the variation of the time component of the metric tensor
in Pre-Planckian Space-time. In doing so, what we lead up to using the Huang Superfluid universe model, which is by the modified superfluid cosmology model leading to examining within the Pre Planckian regime,
Curvature, small but non zero, and energy density
. The Potential energy is given by what it would be if
leading to a relationship of , where we will isolate conditions for the initial time and compare them against a root finder procedure given in another paper written by the author. Then, afterwards, assuming a modified Hubble parameter, with an initial Hubble parameter after the Causal surface with, right after a quantum bounce, determined by
, is then
. And
is an initial degree of freedom value of about 110. Then, the graviton production rate is a function of time leading to a temperature T dependence, with M here is a chosen Mass scale, M of about 30 TeV, with d greater than or equal to zero, representing the Kaluza Klein dimensions assumed with the number of gravitons produced after the onset of Causal structure given by
. This
by Infinite quantum statistics is proportional to entropy. We close with a caveat as far as the implications of all this to the Penrose Conjecture about the vanishing of the Weyl tensor, in the neighborhood of a cosmological initial singularity. And what we think should be put in place instead of the Penrose Weyl tensor hypothesis near a “cosmological” singularity. And we close with a comment about the Weyl curvature tensor, in Pre Planckian to Planckian physics, and also a final appendix on the Mach’s principle as written by Sciama,
in defining the initial space-time non-singular “bubble”.