Using Kiefer Density Matrix for Time Flow Analysis and How This Links to a Proof of Production of Planck Mass BHs during Inflation and Their Resulting Breakup, Leading to a DE Candidate

Andrew Beckwith

doi:10.4236/jhepgc.2021.73059

Abstract

We are using the book “Towards Quantum Gravity” with an article by Claus Kiefer as to a quantum gravity interpretation of the density matrix in the early universe. The density matrix we are using is a one loop approximation, with inflaton value and potential terms, like V (phi) using the Padmanabhan values one can expect if the scale factor is a ~a (Initial) times t ^ gamma. In doing so, we identify two time steps and presume a very small initial time step candidates initial time values which are from a polynomial for time values. A gravity wave analysis concludes our article with inflaton decay, which is finally linked to BHs. And then finally we show using work done by Hawking, et al. how this may give us Planck Sized Black Holes, in the onset of Inflation, with resulting consequences so outlined. A vastly simplified proof of BH masses of Planck mass is presented which ties in directly with issues of the mass of the inflaton initially generated by the 2nd derivative of the effective potential V (phi) at a time t ~4 times Planck time. And we include at the close questions as to DE, and data sets which may give credence to speculation as to different time flow rates at the start and then the conclusion later on, of expansion of our universe. The DE would be created by the breakup of the black holes due to a mechanism brought up by Dr. Freeze in 2012, and we also are using the future works section 8 to define the contours of our DE model which builds upon quite directly the sequence of material from pages 1 to 9 which are cited as to making connection between early universe conditions and the ideas of primordial DE models.

Highlights

What we are doing is to examine several different items of research inquiry 1) The Kieffer Density function is introduced; 2) We ask how to obtain inflaton mass; 3) We establish a probability density mass locator; 4) Applying our ideas above to determining likelihood of Plank sized black holes; 5) Using the existence of relic Black holes, if the break up exists defacto to outline DE initially; 6) And to see if this is linkable eventually to Dr Bakers different rates of time flow theory for the early universe
Our initial goal is to obtain, via a Kieffer Density function candidate minimum time steps which will be for the purpose of giving input into an uncertainty principle of the form [1] [2] [3]
This breakup of black holes by the physics so outlined may give us a way to ascertain if the following entropy, initially is verifiable experimentally, whereas we wish to examine in full ideas given in the series of multiple references

Summary

Introduction

What we are doing is to examine several different items of research inquiry 1) The Kieffer Density function is introduced; 2) We ask how to obtain inflaton mass; 3) We establish a probability density mass locator; 4) Applying our ideas above to determining likelihood of Plank sized black holes; 5) Using the existence of relic Black holes, if the break up exists defacto to outline DE initially; 6) And to see if this is linkable eventually to Dr Bakers different rates of time flow theory for the early universe. The core of the derivation of Equation (4) in [4] due to [7] is dependent on having the following, namely, Quote: 1007 Journal of High Energy Physics, Gravitation and Cosmology

Results

Conclusion