Constraints, in Pre-Planckian Space-Time via Padmabhan’s Λ<sub>initial</sub>·<i>H</i><sup style="margin-left:4px;">-2</sup><sub style="margin-left:-17px;">initial</sub>≈<i>o</i>(1) Approximation Leading to Initial Inflaton Constraints and Its Relation to Early Universe Graviton Production

Abstract

We are looking at what if the initial cosmological constant is inflaton value/squared which supports Corda's assumptions in the Gravity's breath Electronic Journal of theoretical physics article. We close with an idea to be worked in further detail as to density matrices and how it may relate to gravitons traversing from a Pre-Planckian to Planckian space-time regime. We will write up an idea in far greater detail in a future publication.

How to Determine Initial Starting Time Step with an Initial Hubble Parameter H = 0 after Formation of Causal Structure Leading to Investigation of the Penrose Weyl Tensor Conjecture

“…gives a far more detailed proof, and also we can connect it with [56] in terms of an eventual calculation which will be linked to some of the Pre-Planckian spacetime results of [23] and also [47].…”

“…To employ this Equation (5) we are using, as was done in [22], the following boundary condition of the bubble of Space-time as was given in [22] which we put in as being the boundary of a purported quantum bounce. This is also substantially using [23] which using the material so cited.…”

“…What we are doing is to contrast different ways of obtaining a time step ∆t and then employing the tools used in [22] and [23]. This also will be assuming [27], as a given for analysis.…”

Gedanken Experiment for B Field Contributions to Initial Conditions for Relic Graviton Production Based upon an Initial Inflaton Value

“…This adds substance to what was brought up by Beckwith in [16] namely that we have a minimum scale factor of (…”

“…Then if we go to Equation (10) we have a threshold magnetic field for the production of gravitons which looks like if we apply the minimum scale factor condition [16], that ( ) …”